A341806 Number of ways to write n as an ordered sum of 7 nonzero tetrahedral numbers.

1, 0, 0, 7, 0, 0, 21, 0, 0, 42, 0, 0, 77, 0, 0, 126, 0, 0, 168, 7, 0, 211, 42, 0, 252, 105, 0, 252, 182, 0, 245, 315, 0, 231, 469, 0, 175, 574, 21, 140, 735, 105, 105, 854, 210, 56, 875, 315, 42, 987, 525, 21, 952, 693, 7, 882, 840, 42, 924, 1155, 140, 770, 1260, 211, 749, 1470

Offset

7,4

Links

G. C. Greubel, Table of n, a(n) for n = 7..1000

Formula

G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^7.

Mathematica

nmax = 72; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^7, {x, 0, nmax}], x] // Drop[#, 7] &

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 80);
Coefficients(R!( (&+[x^Binomial(j+2, 3): j in [1..20]])^7 )); // G. C. Greubel, Jul 19 2022
(SageMath)
def f(m, x): return ( sum( x^(binomial(j+2, 3)) for j in (1..20) ) )^m
def A341806_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( f(7, x) ).list()
a=A341806_list(100); a[7:81] # G. C. Greubel, Jul 19 2022

Crossrefs

Cf. A000292, A023533, A023670, A282582, A340952, A341778, A341794, A341795, A341796, A341797, A341807, A341808, A341809.

Sequence in context: A356592 A211904 A094898 * A340906 A136115 A061846

Adjacent sequences: A341803 A341804 A341805 * A341807 A341808 A341809

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 20 2021

Status

approved