A358206 Number of ways of making change for n cents using coins of 1, 2, 4, 10 and 20 cents.
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, 93, 93, 112, 112, 134, 134, 159, 159, 187, 187, 218, 218, 252, 252, 292, 292, 335, 335, 384, 384, 436, 436, 494, 494, 558, 558, 628, 628, 704, 704, 786, 786, 874, 874, 972, 972
Offset: 0
Examples
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).
Links
- Index entries for sequences related to making change.
- Index entries for linear recurrences with constant coefficients, 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).
Programs
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Mathematica
A[x_]:=1/((1 - x) (1 - x^2) (1 - x^4) (1 - x^10) (1 - x^20)); a[n_]:=SeriesCoefficient[A[x],{x,0,n}]
Formula
G.f.: 1/((1 - x) (1 - x^2) (1 - x^4) (1 - x^10) (1 - x^20)).
a(n) = A000064(floor(n/2)).
a(n) ~ n^4/38400.
Comments