A074502 a(n) = 1^n + 2^n + 6^n.

3, 9, 41, 225, 1313, 7809, 46721, 280065, 1679873, 10078209, 60467201, 362799105, 2176786433, 13060702209, 78364180481, 470185017345, 2821109972993, 16926659575809, 101559956930561, 609359740534785, 3656158441111553

Offset: 0

Author

Robert G. Wilson v, Aug 23 2002

Keywords

• easy
• nonn

Comments

From Jonathan Vos Post, Apr 16 2005: (Start)

Primes in this sequence include: a(2) = 41, a(10) = 60467201, a(18) = 101559956930561, a(34) = 286511799958070449017978881, a(58) = 1357602166130257152481187563448636039086735361.

Semiprimes in this sequence include: a(1) = 9 = 3^2, a(4) = 1313 = 13 * 101, a(6) = 46721 = 19 * 2459, a(8) = 1679873 = 13 * 129221, a(12) = 2176786433 = 19 * 114567707, a(13) = 13060702209 = 3 * 4353567403, a(28) = 6140942214465083932673 = 13 * 472380170343467994821, a(29) = 36845653286789429854209 = 3 * 12281884428929809951403, a(72) = 106387358923716524807713475752456398462534338499504504833 = 59670762632990981 * 1782905969847563299479030657520813855693. (End)

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-20,12).

Crossrefs

Cf. A001550, A001576, A034513, A001579, A074501 - A074580.

Programs

Mathematica

Table[1^n + 2^n + 6^n, {n, 0, 20}]
LinearRecurrence[{9,-20,12},{3,9,41},30] (* Harvey P. Dale, Aug 15 2017 *)

Formula

G.f.: 1/(1-x)+1/(1-2*x)+1/(1-6*x). E.g.f.: e^x+e^(2*x)+e^(6*x). [Mohammad K. Azarian, Dec 26 2008]

a(n) = 8*a(n-1) - 12*a(n-2) + 5, n> 1. [Gary Detlefs, Jun 21 2010]