A075665 Sum of next n 4th powers.

1, 97, 2177, 23058, 152979, 738835, 2839571, 9191876, 26037717, 66301333, 154762069, 336050870, 686502375, 1331121351, 2467171687, 4396168328, 7566347369, 12628007049, 20504452585, 32481640666, 50320004987, 76392352443, 113852150523, 166836980044, 240712403645

Offset: 1

Author

Zak Seidov, Sep 24 2002

Keywords

• nonn
• easy

Examples

			a(1) = 1^4 = 1; a(2) = 2^4 + 3^4 = 97; a(3) = 4^4 + 5^4 + 6^4 = 2177; a(4) = 7^4 + 8^4 + 9^4 + 10^4 = 23058.
		

Links

• Kelvin Voskuijl, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A000583 (4th powers).

Cf. A006003 (for natural numbers), A072474 (for squares), A075664 - A075671 (3rd to 10th powers), A069876 (n-th powers).

Programs

Mathematica

i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=4; Table[Sum[i^s, {i, i1, i2}], {n, 20}]
Table[Total[Range[(n(n+1))/2+1,((n+1)(n+2))/2]^4],{n,0,20}] (* or *) LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,97,2177,23058,152979,738835,2839571,9191876,26037717,66301333},30] (* Harvey P. Dale, Dec 18 2015 *)

Formula

a(n) = Sum_{i=n*(n-1)/2+1..n*(n-1)/2+n} i^4.

a(n) = (15*n^9 + 90*n^7 + 123*n^5 + 20*n^3 - 8*n)/240. - Charles R Greathouse IV, Sep 17 2009

G.f.: x*(1+87*x+1252*x^2+5533*x^3+8934*x^4+5533*x^5+1252*x^6+87*x^7+x^8)/ (1-x)^10. - Colin Barker, May 25 2012