A146512 Numbers congruent to {1, 3} mod 12.

1, 3, 13, 15, 25, 27, 37, 39, 49, 51, 61, 63, 73, 75, 85, 87, 97, 99, 109, 111, 121, 123, 133, 135, 145, 147, 157, 159, 169, 171, 181, 183, 193, 195, 205, 207, 217, 219, 229, 231, 241, 243, 253, 255, 265, 267, 277, 279, 289, 291, 301, 303, 313, 315, 325, 327

Offset

1,2

Comments

Positive integers k such that Hypergeometric[k/4,(4-k)/4,1/2,3/4] = 2*cos(Pi/6).

Links

David Lovler, Table of n, a(n) for n = 1..1000

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

Formula

a(2k-1) = 12*(k-1)+1, a(2k) = 12*(k-1)+3, where k>0.

With offset 0, a(n) = 8*floor(n/2) + 2*n + 1, or a(n) = 6*n - 1 + 2*(-1)^n. - Gary Detlefs, Mar 13 2010

a(n) = 12*n-a(n-1)-20 (with a(1)=1). - Vincenzo Librandi, Nov 26 2010

G.f.: x * (1 + 2*x + 9*x^2) / (1 - x - x^2 + x^3). - Michael Somos, Dec 06 2016

a(n) = a(n-1)+a(n-2)-a(n-3). - Wesley Ivan Hurt, May 03 2021

E.g.f.: 9 + (6*x - 7)*exp(x) - 2*exp(-x). - David Lovler, Sep 07 2022

Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(3)+1)*(2*Pi + 2*arccosh(26) - 4*sqrt(3)*arccoth(sqrt(3)) + 3*(sqrt(3)-1)*log(3))/48. - Amiram Eldar, Sep 26 2022

Example

G.f. = x + 3*x^2 + 13*x^3 + 15*x^4 + 25*x^5 + 27*x^6 + 37*x^7 + 39*x^8 + ...

Mathematica

Select[Range[300], MemberQ[{1, 3}, Mod[#, 12]]&] (* Ray Chandler, Dec 06 2016 *)

Prog

(PARI) {a(n) = 6*n - 9 + n%2*4}; /* Michael Somos, Dec 06 2016 */

Crossrefs

Cf. A146507, A146509, A146510, A146511.

Sequence in context: A045233 A113487 A032623 * A082704 A353060 A152270

Adjacent sequences: A146509 A146510 A146511 * A146513 A146514 A146515

Keyword

nonn,easy

Author

Artur Jasinski, Oct 30 2008

Extensions

Formula and crossrefs corrected by Ray Chandler, Dec 06 2016

Status

approved