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 A254367 a(n) = 5*2^(n+2) + 2^(2n+2) + 10*3^n + 5^n + 35. 5
 70, 126, 294, 846, 2814, 10326, 40614, 168126, 723534, 3208806, 14570934, 67417806, 316645854, 1505245686, 7225414854, 34956689886, 170199537774, 832952952966, 4093454620374, 20184631056366, 99800366967294, 494533989722646, 2454868429675494 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This is the sequence of fifth terms of "fourth partial sums of m-th powers". 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 (15,-85,225,-274,120). FORMULA a(n) = 15*a(n-1)-85*a(n-2)+225*a(n-3)-274*a(n-4)+120*a(n-5). - Colin Barker, Jan 30 2015 G.f.: -2*(2972*x^4-4302*x^3+2177*x^2-462*x+35) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Jan 30 2015 MATHEMATICA Table[5 2^(n + 2) + 2^(2 n + 2) + 10 3^n + 5^n + 35, {n, 0, 30}] (* Vincenzo Librandi, Feb 02 2015 *) PROG (PARI) vector(30, n, n--; 5*2^(n+2) + 2^(2*n+2) + 10*3^n + 5^n + 35) \\ Colin Barker, Jan 30 2015 (Magma) [5*2^(n+2)+2^(2*n+2)+10*3^n+5^n+35: n in [0..30]]; // Vincenzo Librandi, Feb 02 2015 CROSSREFS Cf. A140504, A254365, A254366. Sequence in context: A039542 A024748 A024756 * A113928 A160354 A215111 Adjacent sequences: A254364 A254365 A254366 * A254368 A254369 A254370 KEYWORD nonn,easy AUTHOR Luciano Ancora, Jan 30 2015 STATUS approved

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Last modified May 21 07:02 EDT 2024. Contains 372729 sequences. (Running on oeis4.)