|
| |
|
|
A228137
|
|
Numbers that are congruent to {1, 4} mod 12.
|
|
2
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
