OFFSET
0,11
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Daniel Panario, Murat Sahin and Qiang Wang, Generalized Alcuin’s Sequence, The Electronic Journal of Combinatorics, Volume 19, Issue 4 (2012).
Index entries for linear recurrences with constant coefficients, signature (0, 0, 1, 1, 0, 1, -1, 0, 0, -1, 0, -1, 0, 0, -1, 1, 0, 1, 1, 0, 0, -1).
FORMULA
a(n) = p_4(n/3) if n == 0 mod 3,
a(n) = p_4((n+8)/3) if n == 1 mod 3,
a(n) = p_4((n+4)/3) if n == 2 mod 3,
where p_4(n) is the number of partitions of n into exactly 4 parts.
EXAMPLE
a(57) = p_4(57/3) = p_4(19) = A001400(15) = 54,
a(58) = p_4((58+8)/3) = p_4(22) = A001400(18) = 84,
a(59) = p_4((59+4)/3) = p_4(21) = A001400(17) = 72,
a(60) = p_4(60/3) = p_4(20) = A001400(16) = 64,
a(61) = p_4((61+8)/3) = p_4(23) = A001400(19) = 94,
a(62) = p_4((62+4)/3) = p_4(22) = A001400(18) = 84.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 06 2017
STATUS
approved