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

Author

Vincenzo Librandi, Jun 12 2018

Keywords

• nonn
• easy
• less

Links

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

Crossrefs

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

Programs

Magma

[n: n in [0..300] | n mod 12 in [1,3,11]]; // 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 *)

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

Extensions

Edited by Bruno Berselli, Jun 13 2018