A254467 a(n) = 15*4^n + 70*2^n + 35*3^n + 5^(n+1) + 6^n + 126.
252, 462, 1122, 3432, 12342, 49632, 216342, 1001952, 4863462, 24500352, 127161462, 676195872, 3668030982, 20227217472, 113076824982, 639383508192, 3649985092902, 21003583828992, 121677813214902, 708891056106912, 4149610383537222
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 (21,-175,735,-1624,1764,-720).
Programs
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Mathematica
Table[15×4^n+70×2^n+35×3^n+5^(n+1)+6^n+126, {n, 0, 25}] (* Michael De Vlieger, Jan 31 2015 *) LinearRecurrence[{21,-175,735,-1624,1764,-720},{252,462,1122,3432,12342,49632},30] (* Harvey P. Dale, Jul 16 2018 *) -
PARI
vector(30, n, n--; 15*4^n + 70*2^n + 35*3^n + 5^(n+1) + 6^n + 126) \\ Colin Barker, Jan 31 2015
Formula
G.f.: -6*(21310*x^5 -34383*x^4 +20750*x^3 -5920*x^2 +805*x -42) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)). - Colin Barker, Jan 31 2015
a(n) = 21*a(n-1)-175*a(n-2)+735*a(n-3)-1624*a(n-4)+1764*a(n-5)-720*a(n-6). - Colin Barker, Jan 31 2015
Comments