A253636 Second partial sums of eighth powers (A001016).
1, 258, 7076, 79430, 542409, 2685004, 10592400, 35277012, 103008345, 270739678, 652829892, 1464901802, 3092704433, 6196296120, 11862778432, 21824228040, 38761435089, 66718602714, 111659333380, 182200064046, 290563654073, 453803117636, 695353566480, 1046979329500
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- Luciano Ancora, Recurrence relation for the second partial sums of m-th powers
- Luciano Ancora, Second partial sums of the m-th powers
- Feihu Liu, Guoce Xin, and Chen Zhang, Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS, arXiv:2412.18744 [math.CO], 2024. See p. 13.
- Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
Programs
-
GAP
List([1..30], n-> n*(n+1)^2*(n+2)*(2*n^6 +12*n^5 +17*n^4 -12*n^3 -19*n^2 +18*n -3)/180); # G. C. Greubel, Aug 28 2019
-
Magma
[n*(n+1)^2*(n+2)*(2*n^6+12*n^5+17*n^4-12*n^3-19*n^2+18*n-3)/180: n in [1..25]]; // Bruno Berselli, Jan 08 2015
-
Maple
seq(n*(n+1)^2*(n+2)*(2*n^6 +12*n^5 +17*n^4 -12*n^3 -19*n^2 +18*n -3))/180, n=1..30); # G. C. Greubel, Aug 28 2019
-
Mathematica
Table[n(n+1)^2(n+2)(2n^6 +12n^5 +17n^4 -12n^3 -19n^2 +18n -3)/180, {n,30}] (* Bruno Berselli, Jan 08 2015 *) Nest[Accumulate,Range[30]^8,2] (* or *) LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{1,258,7076,79430,542409,2685004,10592400, 35277012, 103008345,270739678,652829892},30] (* Harvey P. Dale, Jul 02 2017 *) -
PARI
a(n)=(2*n^10+20*n^9+75*n^8+120*n^7+42*n^6-84*n^5-50*n^4+40*n^3+21*n^2-6*n)/180 \\ Charles R Greathouse IV, Sep 08 2015
-
Sage
[(2*n^10+20*n^9+75*n^8+120*n^7+42*n^6-84*n^5-50*n^4+40*n^3+21*n^2-6*n)/180 for n in [1..24]] # Tom Edgar, Jan 07 2015
Formula
a(n) = (2*n^10 + 20*n^9 + 75*n^8 + 120*n^7 + 42*n^6 - 84*n^5 - 50*n^4 + 40*n^3 + 21*n^2 - 6*n)/180.
a(n) = 2*a(n-1) - a(n-2) + n^8. - Robert Israel, Jan 07 2015
G.f.: x*(1 + x)*(1 + 246*x + 4047*x^2 + 11572*x^3 + 4047*x^4 + 246*x^5 + x^6) / (1 - x)^11. - Bruno Berselli, Jan 08 2015
Comments