A305859 Numbers that are congruent to {1, 3, 11} mod 12.

1, 3, 11, 13, 15, 23, 25, 27, 35, 37, 39, 47, 49, 51, 59, 61, 63, 71, 73, 75, 83, 85, 87, 95, 97, 99, 107, 109, 111, 119, 121, 123, 131, 133, 135, 143, 145, 147, 155, 157, 159, 167, 169, 171, 179, 181, 183, 191, 193, 195, 203, 205, 207, 215, 217, 219, 227, 229, 231, 239

Offset

1,2

Links

Table of n, a(n) for n=1..60.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

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

a(n) = a(n-1) + a(n-3) - a(n-4) for n>12.

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6) for n>6.

a(n) = 2*n + 6*floor(n/3) - 1. - Bruno Berselli, Jun 13 2018

Mathematica

Table[2 n + 6 Floor[n/3] - 1, {n, 1, 60}] (* Bruno Berselli, Jun 13 2018 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 3, 11, 13}, 60] (* Harvey P. Dale, Mar 15 2023 *)

Prog

(Magma) [n: n in [0..300] | n mod 12 in [1, 3, 11]]; // Bruno Berselli, Jun 13 2018

Crossrefs

Equals 2*A047240 - 1 and 2*A047266 + 1 (after 0).

Sequence in context: A119231 A177335 A031449 * A090260 A179522 A020635

Adjacent sequences: A305856 A305857 A305858 * A305860 A305861 A305862

Keyword

nonn,easy,less

Author

Vincenzo Librandi, Jun 12 2018

Extensions

Edited by Bruno Berselli, Jun 13 2018

Status

approved