A220653 a(n) = n^11 + 11*n + 11^n.

1, 23, 2191, 178511, 4208989, 48989231, 364568683, 1996813991, 8804293561, 33739007399, 125937424711, 570623341343, 3881436747541, 36314872538111, 383799398753059, 4185897925275191, 45967322049616753, 505481300395601591, 5559981581902310911, 61159206938673444719

Offset: 0

Author

Jonathan Vos Post, Dec 17 2012

Keywords

• nonn
• easy

Comments

This is to A220425 as 11 is to 2, to A220509 as 11 is to 3, to A220511 as 11 is to 5, and to A220528 as 11 is to 7.

The subsequence of primes begins: 23, 4185897925275191, see A220787 for the associated n.

Examples

			a(1) = 1^11 + 11*1 + 11^1 = 23.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Crossrefs

Cf. A008455, A008593, A001020, A220425, A220509, A220511, A220528, A220787.

Programs

Mathematica

Table[n^11 + 11*n + 11^n, {n, 0, 30}] (* T. D. Noe, Dec 17 2012 *)

Maxima

A220653(n):=n^11+11*n+11^n$ makelist(A220653(n),n,0,20); /* Martin Ettl, Dec 17 2012 */

Formula

a(n) = A008455(n) + A008593(n) + A001020(n).

G.f.: (131*x^12 +21186*x^11 +1682460*x^10 [phone]*x^9 [phone]*x^8 [phone]*x^7 [phone]*x^6 [phone]*x^5 -518211*x^4 -131726*x^3 -1860*x^2 -1) / ((x -1)^12*(11*x -1)). - Colin Barker, May 09 2013

Extensions

a(19) from Stefano Spezia, May 03 2025