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calendar
2021
cover/jan/feb/mar/apr/may/jun/jul/aug/sep/oct/nov/dec
- Cover A271999
- Halogen sequence (the atomic numbers of the elements in group 17 in the periodic table).
- 1, 11, 17, 35, 53, 85, 117, ...
- a(21) = 2021
- January A248431
- Number of length n+2 0..6 arrays with every three consecutive terms having the sum of some two elements equal to twice the third.
- 61, 105, 185, 327, 601, 1105, ...
- a(7) = 2021
- February A325250
- Number of integer partitions of n whose omega-sequence is strict (no repeated parts). The omega-sequence of an integer partition is the sequence of lengths of the multisets obtained by repeatedly taking the multiset of multiplicities until a singleton is reached.
- 1, 1, 2, 2, 3, 2, 5, 2, 5, 4, ...
- a(43) = 2021
- March A238220
- The total number of 5's in all partitions of n into an even number of distinct parts.
- 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, ...
- a(60) = 2021
- a(36) = 120 depicted
- April A266543
- Number of n X 4 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.
- 2, 4, 6, 12, 16, 27, 36, 57, ...
- a(21) = 2021
- May A025149
- Number of partitions of n into distinct parts >= 4.
- 1, 0, 0, 0, 1, 1, 1, 1, 1, 2, ...
- a(61) = 2021
- a(36) = 120 depicted
- June A005816
- Number of 4-valent labeled graphs with n nodes where multiple edges and loops are allowed. Each node has 4 ends of edges and the order of the nodes is significant.
- 1, 1, 3, 15, 138, 2021, ...
- a(5) = 2021
- a(4) = 138 depicted
- July A150600
- Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 0, 0), (0, 1, 1), (1, 0, -1), (1, 0, 1)}. None of the X,Y,Z coordinates can go negative.
- 1, 2, 7, 27, 109, 462, 2021, ...
- a(6) = 2021
- August A283528
- The number of phi-partitions of n. The number of partitions n = a1 + a2 + ... + ak which have at least two parts and obey phi(n) = phi(a1) + phi(a2) + ... + phi(ak). phi is Euler's totient, the number of positive integers up to a given integer that are relatively prime to it.
- 0, 0, 1, 1, 2, 0, 3, 4, 8, 2, ...
- a(49) = 2021
- September A309692
- Sum of the odd parts appearing among the largest parts of the partitions of n into 3 parts.
- 0, 0, 0, 1, 0, 3, 3, 11, 8, ...
- a(44) = 2021
- October A322439
- Number of ordered pairs of integer partitions of n where no part of the first is greater than any part of the second.
- 1, 1, 3, 5, 11, 15, 33, 42, ...
- a(16) = 2021
- November A326540
- Sum of all the parts in the partitions of n into 9 primes.
- 0, ..., 0, 18, 19, 20, 42, ...
- a(43) = 2021
- December A260744
- Number of prime juggling patterns of period n using 2 balls. A prime juggling pattern repeats without visiting the same state more than once.
- 1, 2, 5, 10, 23, 48, 105, ...
- a(11) = 2021
Each of the 13 designs (12 months plus cover) is based on a sequence from the Online Encyclopedia of Integer Sequences® in which the number 2021 occurs. OEIS is a registered trademark of the OEIS Foundation, Inc. This project is neither endorsed by nor affiliated with the OEIS.
The source code will be made available some time in 2021, implemented in Haskell and C without any special libraries:
git clone https://code.mathr.co.uk/oeis-diagrams.git
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