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A085502 Number of (unordered) ways of making change for n dollars using coins of denominations 1, 5, 10, 25, 50 and 100. 2
1, 293, 2728, 12318, 38835, 98411, 215138, 422668, 765813, 1302145, 2103596, 3258058, 4870983, 7066983, 9991430, 13812056, 18720553, 24934173, 32697328, 42283190, 53995291, 68169123, 85173738, 105413348, 129328925, 157399801, 190145268, 228126178, 271946543 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = (n + 1) (80 n^4 + 310 n^3 + 362 n^2 + 121 n + 6) / 6. - Dean Hickerson

From Colin Barker, Feb 21 2017: (Start)

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.

G.f.: (1 + 287*x + 985*x^2 + 325*x^3 + 2*x^4) / (1 - x)^6.

(End)

PROG

(PARI) {a(n)=if(n<0, 0, polcoeff(1/((1-x)*(1-x^5)*(1-x^10)*(1-x^25)*(1-x^50)*(1-x^100))+ x*O(x^n), n))}

for(n=0, 30, print1(a(n*100)", "))

(PARI) Vec((1 + 287*x + 985*x^2 + 325*x^3 + 2*x^4) / (1 - x)^6 + O(x^30)) \\ Colin Barker, Feb 21 2017

CROSSREFS

Cf. A001300.

Sequence in context: A023305 A109182 A241047 * A108828 A239825 A145206

Adjacent sequences:  A085499 A085500 A085501 * A085503 A085504 A085505

KEYWORD

easy,nonn

AUTHOR

Jason Earls, Aug 15 2003

STATUS

approved

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Last modified August 25 13:50 EDT 2019. Contains 326324 sequences. (Running on oeis4.)