

A334464


a(n) is the total number of parts in all partitions of n into consecutive parts that differ by 4.


7



1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 4, 3, 1, 6, 1, 3, 4, 3, 1, 6, 1, 3, 4, 7, 1, 6, 1, 7, 4, 3, 1, 10, 1, 3, 4, 7, 1, 6, 1, 7, 9, 3, 1, 10, 1, 8, 4, 7, 1, 6, 6, 7, 4, 3, 1, 15, 1, 3, 4, 7, 6, 12, 1, 7, 4, 8, 1, 16, 1, 3, 9, 7, 1, 12, 1, 12, 4, 3, 1, 16, 6, 3, 4, 7, 1, 17, 8, 7, 4
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OFFSET

1,6


COMMENTS

The onepart partition n = n is included in the count.
For the relation to hexagonal numbers see also A334462.


LINKS



FORMULA



EXAMPLE

For n = 28 there are three partitions of 28 into consecutive parts that differ by 4, including 28 as a valid partition. They are [28], [16, 12] and [13, 9, 5, 1]. The number of parts of these partitions are 1, 2, 4 respectively. The total number of parts is 1 + 2 + 4 = 7, so a(28) = 7.


MATHEMATICA

nmax = 100;
CoefficientList[Sum[n x^(n(2n1)1)/(1x^n), {n, 1, nmax}]+O[x]^nmax, x] (* JeanFrançois Alcover, Nov 30 2020 *)


PROG

(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, k*x^(k*(2*k1))/(1x^k))) \\ Seiichi Manyama, Dec 04 2020


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



