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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

%I

%S 1,293,2728,12318,38835,98411,215138,422668,765813,1302145,2103596,

%T 3258058,4870983,7066983,9991430,13812056,18720553,24934173,32697328,

%U 42283190,53995291,68169123,85173738,105413348,129328925,157399801,190145268,228126178,271946543

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

%H Colin Barker, <a href="/A085502/b085502.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(n) = (n + 1) (80 n^4 + 310 n^3 + 362 n^2 + 121 n + 6) / 6. - _Dean Hickerson_

%F From _Colin Barker_, Feb 21 2017: (Start)

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

%F (End)

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

%o (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 Cf. A001300.

%K easy,nonn

%O 0,2

%A _Jason Earls_, Aug 15 2003

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Last modified October 21 16:25 EDT 2019. Contains 328302 sequences. (Running on oeis4.)