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A067996
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Number of ways of making change for n cents using coins of 1, 2, 3, 5, 10, 20, 25, 50, 100 cents (all historical U.S.A. coinage from 1 to 100 cents).
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3
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1, 1, 2, 3, 4, 6, 8, 10, 13, 16, 21, 25, 31, 37, 44, 53, 62, 72, 84, 96, 113, 128, 147, 167, 189, 216, 243, 273, 307, 342, 386, 428, 477, 529, 585, 650, 716, 788, 867, 949, 1046, 1141, 1248, 1361, 1481, 1617, 1755, 1904, 2065, 2232, 2424, 2614, 2824, 3045, 3278
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The U.S.A. issued the following unusual denomination coins during the 19th century: 2-cent pieces, 1864-1873; 3-cent pieces, 1851-1889; and 20-cent pieces, 1875-1878.
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REFERENCES
| R. S. Yeoman, A Guide Book of United States Coins, Ed. Kenneth Bressett, 53rd Edition (2000). New York: St. Martin's Press, 1999. pp. 104-106, 135. (also known as The Official Red Book of United States Coins)
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LINKS
| Index entries for sequences related to making change.
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FORMULA
| G.f.: 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^5)*(1-x^10)*(1-x^20)*(1-x^25)*(1-x^50)*(1-x^100))
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EXAMPLE
| a(5)=6 because change can be made for 5 cents in these 6 ways: (1) 5 1-cent coins, (2) 3 1-cent, 1 2-cent, (3) 2 1-cent, 1 3-cent, (4) 1 1-cent, 2 2-cent, (5) 1 2-cent, 1 3-cent, (6) 1 5-cent coin.
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MATHEMATICA
| CoefficientList[ Series[1/((1 - x)(1 - x^2)(1 - x^3)(1 - x^5)(1 - x^10)(1 - x^20)(1 - x^25)(1 - x^50)(1 - x^100)), {x, 0, 55} ], x ]
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PROG
| (PARI) a(n)=polcoeff(1/((1-x)*(1-x^2)*(1-x^3)*(1-x^5)*(1-x^10)*(1-x^20)*(1-x^25)*(1-x^50)*(1-x^100)+x*O(x^n)), n)
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CROSSREFS
| Cf. A067995, A067997, A000008.
Sequence in context: A062435 A171997 A020702 * A027585 A123015 A005434
Adjacent sequences: A067993 A067994 A067995 * A067997 A067998 A067999
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KEYWORD
| easy,nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Feb 07 2002
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