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 A231309 Recurrence a(n) = a(n-2) + n^M for M=10, starting with a(0)=0, a(1)=1. 7
 0, 1, 1024, 59050, 1049600, 9824675, 61515776, 292299924, 1135257600, 3779084325, 11135257600, 29716508926, 73052621824, 167575000775, 362307276800, 744225391400, 1461818904576, 2760219291849, 5032286131200, 8891285549650, 15272286131200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Stanislav Sykora, Table of n, a(n) for n = 0..9999 Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1). FORMULA a(n) = Sum_{k=0..floor(n\2)} (n-2*k)^10. From Colin Barker, Dec 22 2015: (Start) a(n) = 1/66*n*(3*n^10+33*n^9+110*n^8-528*n^6+2112*n^4-4224*n^2+2560). G.f.: x*(1 +1012*x +46828*x^2 +408364*x^3 +901990*x^4 +408364*x^5 +46828*x^6 +1012*x^7 +x^8) / (1 -x)^12. (End) EXAMPLE a(5) = 5^10 + 3^10 + 1^10 = 9824675. PROG (PARI) nmax=100; a=vector(nmax); a[2]=1; for(i=3, #a, a[i]=a[i-2]+(i-1)^10); print(a); (PARI) concat(0, Vec(x*(1 +1012*x +46828*x^2 +408364*x^3 +901990*x^4 +408364*x^5 +46828*x^6 +1012*x^7 +x^8) / (1 -x)^12 + O(x^40))) \\ Colin Barker, Dec 22 2015 CROSSREFS Cf. A001477 (M=1), A000292 (M=2), A105636 (M=3), A231303 (M=4), A231304 (M=5), A231305 (M=6), A231306 (M=7), A231307 (M=8), A231308 (M=9). Sequence in context: A008454 A030629 A056587 * A134847 A066371 A236216 Adjacent sequences:  A231306 A231307 A231308 * A231310 A231311 A231312 KEYWORD nonn,easy AUTHOR Stanislav Sykora, Nov 07 2013 STATUS approved

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