A322856 - OEIS

%I #5 Dec 29 2018 14:33:08

%S 1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,10,12,15,19,24,30,37,45,54,64,76,

%T 91,110,135,166,204,250,305,370,447,539,650,787,956,1164,1419,1730,

%U 2107,2562,3110,3770,4569,5540,6723,8166,9926,12070,14677,17841,21675

%N Number of compositions (ordered partitions) of n into octagonal pyramidal numbers (A002414).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%F G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)*(2*k-1)/2)).

%t nmax = 56; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (2 k - 1)/2), {k, 1, nmax}]), {x, 0, nmax}], x]

%Y Cf. A002414, A279224, A280863, A282582, A322340, A322800, A322853, A322854, A322855.

%K nonn

%O 0,10

%A _Ilya Gutkovskiy_, Dec 29 2018