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Search: id:A160551
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| A160551 |
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Number of (unordered) ways of making change for n dollars using coins of denominations 1, 5, 10, and 25. |
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+0
1
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| 1, 242, 1463, 4464, 10045, 19006, 32147, 50268, 74169, 104650, 142511, 188552, 243573, 308374, 383755, 470516, 569457, 681378, 807079, 947360, 1103021
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The nth value is the number of distinct quadruplets (p, n, d, q) of nonnegative integers satisfying p + 5n + 10d + 25q = 100n.
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FORMULA
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a(n) is the coefficient of x^(100n) in f(x)=1/((1-x)(1-x^5)(1-x^10)(1-x^25))
a(n) = (3 + 53*n + 270*n^2 + 400*n^3) / 3
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EXAMPLE
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There are four ways to make $0.10: (1) 10 pennies, (2) 5 pennies and 1 nickel, (3) 2 nickels, and (4) 1 dime.
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MAPLE
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f := 1/(1-x)/(1-x^5)/(1-x^10)/(1-x^25); a := n -> (convert(series(f, x, 100*n+1), polynom)-convert(series(f, x, 100*n), polynom)) /x^(100*n);
a := n -> (3 + 53*n + 270*n^2 + 400*n^3) / 3;
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CROSSREFS
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Sequence in context: A023703 A094908 A070284 this_sequence A006601 A035748 A022153
Adjacent sequences: A160548 A160549 A160550 this_sequence A160552 A160553 A160554
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KEYWORD
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easy,nonn
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AUTHOR
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Lee A. Newberg (integer(AT)quantconsulting.com), May 18 2009, Jun 15 2009
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