A341791 -id:A341791 - cp's OEIS frontend

A341807 Number of ways to write n as an ordered sum of 8 nonzero tetrahedral numbers.

1, 0, 0, 8, 0, 0, 28, 0, 0, 64, 0, 0, 126, 0, 0, 224, 0, 0, 336, 8, 0, 456, 56, 0, 589, 168, 0, 672, 336, 0, 708, 616, 0, 728, 1016, 0, 658, 1400, 28, 560, 1856, 168, 476, 2352, 420, 336, 2632, 728, 238, 2968, 1260, 168, 3192, 1904, 84, 3096, 2464, 112, 3192, 3360, 308, 3024, 4144

Offset: 8

Ilya Gutkovskiy, Feb 20 2021

nonn

G. C. Greubel, Table of n, a(n) for n = 8..1000

Cf. A000292, A023533, A023670, A282582, A340953, A341791, A341794, A341795, A341796, A341797, A341806, A341808, A341809.

R:=PowerSeriesRing(Integers(), 80);
Coefficients(R!( (&+[x^Binomial(j+2,3): j in [1..70]])^8 )); // G. C. Greubel, Jul 19 2022

nmax = 70; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^8, {x, 0, nmax}], x] // Drop[#, 8] &

def f(m, x): return ( sum( x^(binomial(j+2,3)) for j in (1..8) ) )^m
def A341807_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( f(8, x) ).list()
a=A341807_list(100); a[8:81] # G. C. Greubel, Jul 19 2022

G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^8.

A341792 Number of partitions of n into 9 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, 3, 2, 0, 3, 3, 0, 3, 4, 1, 3, 4, 1, 2, 5, 1, 3, 5, 2, 2, 5, 2, 2, 5, 3, 2, 7, 4, 3, 6, 4, 2, 6, 4, 3, 7, 5, 3, 6, 5, 3, 6, 6, 4, 7, 7, 5, 7, 7, 3, 7, 7, 5, 7, 9, 4, 7, 9, 5, 6, 10, 5, 8

Offset: 9

Ilya Gutkovskiy, Feb 19 2021

nonn

Cf. A000292, A023533, A024692, A068980, A319819, A341774, A341775, A341776, A341777, A341778, A341791, 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

A341807 Number of ways to write n as an ordered sum of 8 nonzero tetrahedral numbers.

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A341792 Number of partitions of n into 9 nonzero tetrahedral numbers.

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

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