A075671 Sum of next n 10th powers.

1, 60073, 71280377, 14843001474, 1091618326275, 39736919990851, 870012241054523, 12967387960026452, 143075291905145949, 1240006139651007925, 8817026830146599701, 53151169903167142598, 278615540073819826527, 1295610629596485350799, 5430916505417064431575

Offset: 1

Author

Zak Seidov, Sep 24 2002

Keywords

• nonn
• easy

Examples

			a(1) = 1^10 = 1; a(2) = 2^10 + 3^10 = 60073; a(3) = 4^10 + 5^10 + 6^10 = 71280377; a(4) = 7^10 + 8^10 + 9^10 + 10^10 = 14843001474.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (22, -231, 1540, -7315, 26334, -74613, 170544, -319770, 497420, -646646, 705432, -646646, 497420, -319770, 170544, -74613, 26334, -7315, 1540, -231, 22, -1).

Crossrefs

Cf. A008454 (10th powers).

Cf. A072474 (for squares), A075664 - A075670 (3rd to 9th powers), A069876 (n-th powers).

Programs

Mathematica

i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=10; Table[Sum[i^s, {i, i1, i2}], {n, 20}]
With[{nn=20},Total/@TakeList[Range[(nn(nn+1))/2]^10,Range[nn]]] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Mar 18 2018 *)

Formula

a(n) = Sum_{i=n(n-1)/2+1..n(n-1)/2+n} i^10.

a(n) = (33n^21 + 825n^19 + 6336n^17 + 18546n^15 + 14289n^13 - 14187n^11 - 418n^9 + 20592n^7 - 10560n^5 - 4224n^3 + 2560n)/33792. - Charles R Greathouse IV, Sep 17 2009

G.f.: (x^20 +60051*x^19 [phone]*x^18 [phone]*x^17 [phone]*x^16 [phone]*x^15 [phone]*x^14 +1431958892640624*x^13 +5170348336132746*x^12 +11021721646301518*x^11 +14154518527431996*x^10 +11021721646301518*x^9 +5170348336132746*x^8 +1431958892640624*x^7 [phone]*x^6 [phone]*x^5 [phone]*x^4 [phone]*x^3 [phone]*x^2 +60051*x +1) / (x -1)^22. - Colin Barker, Dec 19 2012

Extensions

More terms from Colin Barker, Dec 19 2012