[go: up one dir, main page]

login
A081055
Number of partitions of 2n in which no parts are multiples of 4.
4
1, 2, 4, 9, 16, 29, 50, 82, 132, 208, 320, 484, 722, 1060, 1539, 2210, 3138, 4416, 6163, 8528, 11716, 15986, 21666, 29190, 39104, 52098, 69060, 91106, 119634, 156416, 203664, 264128, 341256, 439321, 563600, 720648, 918530, 1167154, 1478720
OFFSET
0,2
COMMENTS
Euler transform of period 16 sequence [2,1,3,1,3,0,2,0,2,0,3,1,3,1,2,0,...].
LINKS
FORMULA
G.f.: (sum_{n>=0} x^A074378(n))/(sum_n (-x)^n^2).
a(n) = A001935(2n).
a(n) ~ exp(Pi*sqrt(n)) / (2^(7/2) * n^(3/4)). - Vaclav Kotesovec, Nov 15 2017
MATHEMATICA
Table[Count[IntegerPartitions[2n], x_ /; ! MemberQ [Mod[x, 4], 0, 2] ], {n, 0, 38}] (* Robert Price, Jul 28 2020 *)
PROG
(PARI) a(n)=local(X); if(n<0, 0, X=x+x*O(x^(2*n)); polcoeff(eta(X^4)/eta(X), 2*n))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael Somos, Mar 03 2003
STATUS
approved