A075666 Sum of next n 5th powers.

1, 275, 11925, 208624, 2078375, 14118201, 72758875, 304553600, 1084203549, 3390961375, 9540835601, 24582546000, 58801331875, 131987718149, 280410672375, 567799960576, 1102105900025, 2060382328875, 3724847929549, 6534040766000, 11154010982751, 18575718271825

Offset: 1

Author

Zak Seidov, Sep 24 2002

Keywords

• nonn
• easy

Examples

			a(1) = 1^5 = 1; a(2) = 2^5 + 3^5 = 275; a(3) = 4^5 + 5^5 + 6^5 = 11925; a(4) = 7^5 + 8^5 + 9^5 + 10^5 = 208624.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Crossrefs

Cf. A000584 (5th powers).

Cf. 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=5; Table[Sum[i^s, {i, i1, i2}], {n, 20}]
nn=30;With[{p5=Range[((nn+1)(nn+2))/2]^5},Join[{1},Table[Total[Take[p5,{(n(n+1))/2+1,((n+1)(n+2))/2}]],{n,nn}]]] (* Harvey P. Dale, Mar 09 2014 *)
Module[{nn=25,p5},p5=Range[(nn(nn+1))/2]^5;Total/@TakeList[p5,Range[nn]]] (* Harvey P. Dale, Oct 13 2023 *)

Formula

a(n) = Sum_{i=n(n-1)/2+1..n(n-1)/2+n} i^5.

a(n) = (3n^11 + 25n^9 + 53n^7 + 23n^5 - 8n^3)/96. - Charles R Greathouse IV, Sep 17 2009

G.f.: x*(x^10 +263*x^9 +8691*x^8 +83454*x^7 +301932*x^6 +458718*x^5 +301932*x^4 +83454*x^3 +8691*x^2 +263*x+1) / (x-1)^12. - Colin Barker, Jul 22 2012