%I #5 Oct 01 2022 00:37:23
%S 1,1,2,3,6,10,18,31,56,98,174,306,542,956,1690,2983,5272,9310,16448,
%T 29050,51318,90644,160118,282826,499590,882468,1558798,2753448,
%U 4863696,8591212,15175514,26805984,47350057,83639033,147739853,260967374,460972308,814260589
%N Number of compositions (ordered partitions) of n into pentanacci numbers 1,2,4,8,16,31, ... (A001591).
%F G.f.: 1 / (1 - Sum_{k>=5} x^A001591(k)).
%t A001591[0] = A001591[1] = A001591[2] = A001591[3] = 0; A001591[4] = 1; A001591[n_] := A001591[n] = A001591[n - 1] + A001591[n - 2] + A001591[n - 3] + A001591[n - 4] + A001591[n - 5]; nmax = 37; CoefficientList[Series[1/(1 - Sum[x^A001591[k], {k, 5, 20}]), {x, 0, nmax}], x]
%Y Cf. A001591, A076739, A288120, A357451, A357453, A357454.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 29 2022