A017641 a(n) = 12*n + 10.

10, 22, 34, 46, 58, 70, 82, 94, 106, 118, 130, 142, 154, 166, 178, 190, 202, 214, 226, 238, 250, 262, 274, 286, 298, 310, 322, 334, 346, 358, 370, 382, 394, 406, 418, 430, 442, 454, 466, 478, 490, 502, 514, 526, 538, 550, 562, 574, 586, 598, 610, 622, 634

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Exponents e such that x^e + x^2 - 1 is reducible.

If Y is a 4-subset of an (2n+1)-set X then, for n>=3, a(n-2) is the number of 3-subsets of X having at least two elements in common with Y. - Milan Janjic, Dec 16 2007

Links

• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A008594, A016969, A017533, A017545, A017593, A030132.

Programs

Mathematica

Range[10, 1000, 12] (* Vladimir Joseph Stephan Orlovsky, May 29 2011 *)

PARI

a(n)=12*n+10 \\ Charles R Greathouse IV, Jul 10 2016

Formula

A030132(a(n)) = 9. - Reinhard Zumkeller, Jul 04 2007

G.f.: 2*(5 + x)/(1 - x)^2. - Stefano Spezia, May 09 2021

Sum_{n>=0} (-1)^n/a(n) = Pi/12 - sqrt(3)*log(2 + sqrt(3))/12. - Amiram Eldar, Dec 12 2021

From Elmo R. Oliveira, Apr 04 2025: (Start)

E.g.f.: 2*exp(x)*(5 + 6*x).

a(n) = 2*A016969(n).

a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)