A001310 -id:A001310 - cp's OEIS frontend

A339094 Number of (unordered) ways of making change for n US Dollars using the current US denominations of $1, $2, $5, $10, $20, $50 and $100 bills.

1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 11, 12, 15, 16, 19, 22, 25, 28, 31, 34, 41, 44, 51, 54, 61, 68, 75, 82, 89, 96, 109, 116, 129, 136, 149, 162, 175, 188, 201, 214, 236, 249, 271, 284, 306, 328, 350, 372, 394, 416, 451, 473, 508, 530, 565, 600, 635, 670, 705, 740, 793, 828, 881, 916

Offset: 0

Robert G. Wilson v, Nov 25 2020

Not the same as A001313. First difference appears at A001313(100) being 4562, whereas a(100) is 4563; obviously one more than A001313(100).
Not the same as A057537.
Number of partitions of n into parts 1, 2, 5, 10, 20, 50 and 100.

			a(5) is 4 because 1+1+1+1+1 = 2+1+1+1 = 2+2+1 = 5.

Cf. A000008, A001299, A001300, A001301, A001306, A001302, A001306, A001310, A001312, A001313, A001314, A001319, A001343, A001362, A001364, A057537, A067996, A067997, A073031, A085502, A112024, A124146, A160551, A169718, A181934, A187243.

f[n_] := Length@ IntegerPartitions[n, All, {1, 2, 5, 10, 20, 50, 100}]; Array[f, 75, 0] (* or *)
CoefficientList[ Series[1/((1 - x) (1 - x^2) (1 - x^5) (1 - x^10) (1 - x^20) (1 - x^50) (1 - x^100)), {x, 0, 75}], x] (* or *)
Table[ Length@ FrobeniusSolve[{1, 2, 5, 10, 20, 50, 100}, n], {n, 0, 75}] (* much slower *)

coins(v[..])=my(x='x); prod(i=1, #v, 1/(1-x^v[i]))
Vec(coins(1, 2, 5, 10, 20, 50, 100)+O(x^99)) \\ Charles R Greathouse IV, Jan 24 2022

G.f.: 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^10)*(1-x^20)*(1-x^50)*(1-x^100)).

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

Original entry on oeis.org

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

Daniel Checa, Nov 03 2022

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

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

			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).

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).

Cf. A000064, A001310.

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}]

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.

cp's OEIS Frontend

A339094 Number of (unordered) ways of making change for n US Dollars using the current US denominations of $1, $2, $5, $10, $20, $50 and $100 bills.

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