login
A085502
Number of (unordered) ways of making change for n dollars using coins of denominations 1, 5, 10, 25, 50 and 100.
3
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
OFFSET
0,2
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: A109182 A342874 A241047 * A108828 A239825 A145206
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Aug 15 2003
STATUS
approved