A341792 -id:A341792 - cp's OEIS frontend

A341808 Number of ways to write n as an ordered sum of 9 nonzero tetrahedral numbers.

1, 0, 0, 9, 0, 0, 36, 0, 0, 93, 0, 0, 198, 0, 0, 378, 0, 0, 624, 9, 0, 918, 72, 0, 1269, 252, 0, 1597, 576, 0, 1836, 1134, 0, 2025, 2025, 0, 2058, 3096, 36, 1926, 4356, 252, 1764, 5877, 756, 1470, 7182, 1512, 1134, 8388, 2772, 882, 9576, 4608, 588, 10035, 6552, 462

Offset: 9

Ilya Gutkovskiy, Feb 20 2021

nonn

G. C. Greubel, Table of n, a(n) for n = 9..1000

Cf. A000292, A023533, A023670, A282582, A340954, A341792, A341794, A341795, A341796, A341797, A341806, A341807, A341809.

R:=PowerSeriesRing(Integers(), 70);
Coefficients(R!( (&+[x^Binomial(j+2,3): j in [1..70]])^9 )); // G. C. Greubel, Jul 18 2022

nmax = 66; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^9, {x, 0, nmax}], x] // Drop[#, 9] &

def f(m, x): return ( sum( x^(binomial(j+2,3)) for j in (1..8) ) )^m
def A341808_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( f(9, x) ).list()
a=A341808_list(100); a[9:71] # G. C. Greubel, Jul 18 2022

G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^9.

A341791 Number of partitions of n into 8 nonzero tetrahedral numbers.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 3, 1, 0, 3, 1, 0, 3, 1, 0, 3, 2, 0, 3, 2, 0, 2, 3, 0, 3, 4, 1, 2, 4, 1, 2, 4, 1, 2, 5, 2, 2, 4, 2, 1, 5, 3, 2, 6, 4, 2, 5, 3, 2, 5, 4, 2, 6, 4, 3, 5, 5, 2, 5, 5, 4, 6, 6, 3, 6, 6, 3, 5, 6, 3, 6, 8, 4, 5, 8, 4, 5, 8, 4, 5, 10

Offset: 8

Ilya Gutkovskiy, Feb 19 2021

nonn

Cf. A000292, A023533, A024692, A068980, A319818, A341774, A341775, A341776, A341777, A341778, A341792, A341793.

A341793 Number of partitions of n into 10 nonzero tetrahedral numbers.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 3, 1, 0, 3, 1, 0, 3, 1, 0, 4, 2, 0, 4, 2, 0, 3, 3, 0, 4, 4, 1, 3, 4, 1, 3, 5, 1, 3, 6, 2, 3, 5, 2, 2, 6, 3, 3, 7, 4, 3, 7, 4, 3, 7, 5, 3, 8, 5, 4, 7, 6, 3, 7, 6, 5, 8, 8, 5, 8, 8, 5, 8, 8, 5, 9, 10, 6, 8, 10, 5, 8, 11, 7

Offset: 10

Ilya Gutkovskiy, Feb 19 2021

nonn

Cf. A000292, A023533, A024692, A068980, A319820, A341774, A341775, A341776, A341777, A341778, A341791, A341792.

cp's OEIS Frontend

A341808 Number of ways to write n as an ordered sum of 9 nonzero tetrahedral numbers.

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A341791 Number of partitions of n into 8 nonzero tetrahedral numbers.

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A341793 Number of partitions of n into 10 nonzero tetrahedral numbers.

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