A228137 Numbers that are congruent to {1, 4} mod 12.

1, 4, 13, 16, 25, 28, 37, 40, 49, 52, 61, 64, 73, 76, 85, 88, 97, 100, 109, 112, 121, 124, 133, 136, 145, 148, 157, 160, 169, 172, 181, 184, 193, 196, 205, 208, 217, 220, 229, 232, 241, 244, 253, 256, 265, 268, 277, 280, 289, 292, 301, 304, 313, 316, 325

Offset

1,2

Comments

The squares of the terms of A001651 are the squares of this sequence. - Bruno Berselli, Aug 12 2013

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = -13/2 - 3*(-1)^n/2 + 6*n.

a(n) = a(n-1) + a(n-2) - a(n-3).

G.f.: x*(8*x^2+3*x+1) / ((x-1)^2*(x+1)).

Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(3)+3)*Pi/36 + log(2)/4 - sqrt(3)*log(26-15*sqrt(3))/36. - Amiram Eldar, Dec 28 2021

E.g.f.: 8 + ((12*x - 13)*exp(x) - 3*exp(-x))/2. - David Lovler, Sep 04 2022

Mathematica

Select[Range[300], MemberQ[{1, 4}, Mod[#, 12]] &] (* Amiram Eldar, Dec 28 2021 *)

Prog

(PARI) Vec(x*(8*x^2+3*x+1)/((x-1)^2*(x+1)) + O(x^99))

Crossrefs

Cf. A001651, A087445, A146512, A228138.

Sequence in context: A074262 A297363 A031208 * A301965 A191135 A268524

Adjacent sequences: A228134 A228135 A228136 * A228138 A228139 A228140

Keyword

nonn,easy

Author

Colin Barker, Aug 12 2013

Status

approved