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

1,2

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).

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

Example

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.

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 *)

Crossrefs

Cf. A000583 (4th powers).

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

Sequence in context: A241968 A020538 A359639 * A012839 A379508 A017813

Adjacent sequences: A075662 A075663 A075664 * A075666 A075667 A075668

Keyword

nonn,easy

Author

Zak Seidov, Sep 24 2002

Status

approved