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A160551 Number of unordered ways of making change for n dollars using coins of denominations 1, 5, 10, and 25. 3
1, 242, 1463, 4464, 10045, 19006, 32147, 50268, 74169, 104650, 142511, 188552, 243573, 308374, 383755, 470516, 569457, 681378, 807079, 947360, 1103021, 1274862, 1463683, 1670284, 1895465, 2140026, 2404767, 2690488, 2997989, 3328070, 3681531, 4059172, 4461793 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n) is the number of distinct quadruplets (p, k, d, q) of nonnegative integers satisfying p + 5k + 10d + 25q = 100n.
LINKS
FORMULA
a(n) = [x^(100*n)] 1/((1-x)*(1-x^5)*(1-x^10)*(1-x^25)).
a(n) = (3 + 53*n + 270*n^2 + 400*n^3) / 3.
From Alois P. Heinz, Oct 08 2022: (Start)
a(n) = A001299(100*n).
G.f.: (60*x^3+501*x^2+238*x+1)/(x-1)^4. (End)
EXAMPLE
There are four ways to make $0.10: (1) 10 pennies, (2) 5 pennies and 1 nickel, (3) 2 nickels, and (4) 1 dime.
MAPLE
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;
PROG
(PARI) a(n) = {(3 + 53*n + 270*n^2 + 400*n^3) / 3} \\ Andrew Howroyd, Feb 02 2020
CROSSREFS
Cf. A001299.
Sequence in context: A258894 A258887 A234484 * A258886 A354563 A354565
KEYWORD
nonn,easy
AUTHOR
Lee A. Newberg, May 18 2009, Jun 15 2009
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Feb 02 2020
STATUS
approved

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Last modified April 21 17:27 EDT 2024. Contains 371874 sequences. (Running on oeis4.)