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Number of compositions (ordered partitions) of n into tetranacci numbers 1,2,4,8,15,29, ... (A000078).
3

%I #5 Oct 01 2022 00:37:09

%S 1,1,2,3,6,10,18,31,56,98,174,306,542,956,1690,2984,5273,9313,16453,

%T 29062,51340,90689,160203,282994,499908,883078,1559948,2755624,

%U 4867776,8598858,15189770,26832521,47399291,83730207,147908288,261277998,461544073

%N Number of compositions (ordered partitions) of n into tetranacci numbers 1,2,4,8,15,29, ... (A000078).

%F G.f.: 1 / (1 - Sum_{k>=4} x^A000078(k)).

%t A000078[0] = A000078[1] = A000078[2] = 0; A000078[3] = 1; A000078[n_] := A000078[n] = A000078[n - 1] + A000078[n - 2] + A000078[n - 3] + A000078[n - 4]; nmax = 36; CoefficientList[Series[1/(1 - Sum[x^A000078[k], {k, 4, 20}]), {x, 0, nmax}], x]

%Y Cf. A000078, A076739, A287656, A357451, A357452, A357455.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Sep 29 2022