A358206 - OEIS

%I #18 Nov 08 2022 07:57:07

%S 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 93,93,112,112,134,134,159,159,187,187,218,218,252,252,292,292,335,

%U 335,384,384,436,436,494,494,558,558,628,628,704,704,786,786,874,874,972,972

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

%C Number of ways of making change for 50n Colombian pesos using coins of 50, 100, 200, 500 and 1000 pesos.

%C Number of partitions of n into parts 1,2,4,10 and 20.

%H <a href="/index/Mag#change">Index entries for sequences related to making change.</a>

%H <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 G.f.: 1/((1 - x) (1 - x^2) (1 - x^4) (1 - x^10) (1 - x^20)).

%F a(n) = A000064(floor(n/2)).

%F a(n) ~ n^4/38400.

%e 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 A[x_]:=1/((1 - x) (1 - x^2) (1 - x^4) (1 - x^10) (1 - x^20));

%t a[n_]:=SeriesCoefficient[A[x],{x,0,n}]

%Y Cf. A000064, A001310.

%K nonn,easy

%O 0,3

%A _Daniel Checa_, Nov 03 2022