A254468 a(n) = 35*4^n + 126*2^n + 70*3^n + 15*5^n + 5*6^n + 7^n + 210.
462, 924, 2508, 8646, 35112, 159654, 787968, 4137966, 22807752, 130656534, 772253328, 4683193086, 29012227992, 182964472614, 1171328741088, 7594839621006, 49780643849832, 329318254755894, 2195866174387248, 14741498331453726, 99542297086537272
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Luciano Ancora, Demonstration of formulas, page 2.
- Luciano Ancora, Recurrence relations for partial sums of m-th powers
- Index entries for linear recurrences with constant coefficients, signature (28,-322,1960,-6769,13132,-13068,5040).
Programs
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Mathematica
Table[35 4^n + 126 2^n + 70 3^n + 15 5^n + 5 6^n + 7^n + 210, {n, 0, 25}] (* Michael De Vlieger, Jan 31 2015 *) LinearRecurrence[{28,-322,1960,-6769,13132,-13068,5040},{462,924,2508,8646,35112,159654,787968},30] (* Harvey P. Dale, Dec 29 2019 *) -
PARI
vector(30, n, n--; 35*4^n + 126*2^n + 70*3^n + 15*5^n + 5*6^n + 7^n + 210) \\ Colin Barker, Jan 31 2015
Formula
G.f.: -6*(259610*x^6 -461263*x^5 +319473*x^4 -111595*x^3 +20900*x^2 -2002*x +77) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)). - Colin Barker, Jan 31 2015
a(n) = 28*a(n-1) -322*a(n-2) +1960*a(n-3) -6769*a(n-4) +13132*a(n-5) -13068*a(n-6) +5040*a(n-7). - Colin Barker, Jan 31 2015
Comments