cp's OEIS Frontend

A085502 Number of (unordered) ways of making change for n dollars using coins of denominations 1, 5, 10, 25, 50 and 100.

%I A085502 #12 Dec 15 2017 17:36:25
%S A085502 1,293,2728,12318,38835,98411,215138,422668,765813,1302145,2103596,
%T A085502 3258058,4870983,7066983,9991430,13812056,18720553,24934173,32697328,
%U A085502 42283190,53995291,68169123,85173738,105413348,129328925,157399801,190145268,228126178,271946543
%N A085502 Number of (unordered) ways of making change for n dollars using coins of denominations 1, 5, 10, 25, 50 and 100.
%H A085502 Colin Barker, <a href="/A085502/b085502.txt">Table of n, a(n) for n = 0..1000</a>
%H A085502 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A085502 a(n) = (n + 1) (80 n^4 + 310 n^3 + 362 n^2 + 121 n + 6) / 6. - _Dean Hickerson_
%F A085502 From _Colin Barker_, Feb 21 2017: (Start)
%F A085502 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.
%F A085502 G.f.: (1 + 287*x + 985*x^2 + 325*x^3 + 2*x^4) / (1 - x)^6.
%F A085502 (End)
%o A085502 (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))}
%o A085502 for(n=0,30,print1(a(n*100)","))
%o A085502 (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
%Y A085502 Cf. A001300.
%K A085502 easy,nonn
%O A085502 0,2
%A A085502 _Jason Earls_, Aug 15 2003