A341807 - OEIS

%I #12 Jul 20 2022 01:35:50

%S 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,

%T 672,336,0,708,616,0,728,1016,0,658,1400,28,560,1856,168,476,2352,420,

%U 336,2632,728,238,2968,1260,168,3192,1904,84,3096,2464,112,3192,3360,308,3024,4144

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

%H G. C. Greubel, <a href="/A341807/b341807.txt">Table of n, a(n) for n = 8..1000</a>

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

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

%o (Magma)

%o R<x>:=PowerSeriesRing(Integers(), 80);

%o Coefficients(R!( (&+[x^Binomial(j+2,3): j in [1..70]])^8 )); // _G. C. Greubel_, Jul 19 2022

%o (SageMath)

%o def f(m, x): return ( sum( x^(binomial(j+2,3)) for j in (1..8) ) )^m

%o def A341807_list(prec):

%o     P.<x> = PowerSeriesRing(ZZ, prec)

%o     return P( f(8, x) ).list()

%o a=A341807_list(100); a[8:81] # _G. C. Greubel_, Jul 19 2022

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

%K nonn

%O 8,4

%A _Ilya Gutkovskiy_, Feb 20 2021