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A358206 Number of ways of making change for n cents using coins of 1, 2, 4, 10 and 20 cents.

%I A358206 #18 Nov 08 2022 07:57:07
%S A358206 1,1,2,2,4,4,6,6,9,9,13,13,18,18,24,24,31,31,39,39,50,50,62,62,77,77,
%T A358206 93,93,112,112,134,134,159,159,187,187,218,218,252,252,292,292,335,
%U A358206 335,384,384,436,436,494,494,558,558,628,628,704,704,786,786,874,874,972,972
%N A358206 Number of ways of making change for n cents using coins of 1, 2, 4, 10 and 20 cents.
%C A358206 Number of ways of making change for 50n Colombian pesos using coins of 50, 100, 200, 500 and 1000 pesos.
%C A358206 Number of partitions of n into parts 1,2,4,10 and 20.
%H A358206 <a href="/index/Mag#change">Index entries for sequences related to making change.</a>
%H A358206 <a href="/index/Rec#order_37">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1, 1, -1, -1, 1, 0, 0, 1, -1, -1, 1, -1, 1, 1, -1, 0, 0, 1, -1, -1, 1, -1, 1, 1, -1, 0, 0, -1, 1, 1, -1, 1, -1, -1, 1).
%F A358206 G.f.: 1/((1 - x) (1 - x^2) (1 - x^4) (1 - x^10) (1 - x^20)).
%F A358206 a(n) = A000064(floor(n/2)).
%F A358206 a(n) ~ n^4/38400.
%e A358206 a(5)=4 counts the ways of making change for 5 cents, these are (1,1,1,1,1), (1,1,1,2), (1,2,2), (1,4).
%t A358206 A[x_]:=1/((1 - x) (1 - x^2) (1 - x^4) (1 - x^10) (1 - x^20));
%t A358206 a[n_]:=SeriesCoefficient[A[x],{x,0,n}]
%Y A358206 Cf. A000064, A001310.
%K A358206 nonn,easy
%O A358206 0,3
%A A358206 _Daniel Checa_, Nov 03 2022