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A341806 Number of ways to write n as an ordered sum of 7 nonzero tetrahedral numbers. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 27 07:30 EDT 2022. Contains 357052 sequences. (Running on oeis4.)