A179088 Positive integers of the form (2*m^2+1)/11.

3, 9, 41, 59, 123, 153, 249, 291, 419, 473, 633, 699, 891, 969, 1193, 1283, 1539, 1641, 1929, 2043, 2363, 2489, 2841, 2979, 3363, 3513, 3929, 4091, 4539, 4713, 5193, 5379, 5891, 6089, 6633, 6843, 7419, 7641, 8249, 8483, 9123, 9369, 10041, 10299, 11003, 11273

Offset: 1

Author

Bruno Berselli, Jun 29 2010 - Jul 09 2010

Keywords

• nonn
• easy

Comments

Here m = (11*(2*n - 1) - 5*(-1)^n)/4 for n>0.

All terms of A113338 are in the sequence.

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A113338, A179337-A179370.

Programs

Magma

[i/11: m in [1..250] | i mod 11 eq 0 where i is 2*m^2+1]; // Bruno Berselli, Jun 26 2011

Maple

t1:=[]; for n from 0 to 1000 do i:=2*n^2+1; if i mod 11 = 0 then t1:=[op(t1),i/11]; fi; od: # N. J. A. Sloane, Jul 05 2010

Mathematica

Select[Table[(2m^2 + 1)/11, {m, 0, 300}], IntegerQ] (* Harvey P. Dale, Dec 17 2010 *)

PARI

for(m=1, 250, i=2*m^2+1; if(Mod(i,11)==0, print1(i/11", "))); \\ Bruno Berselli, Jun 26 2011

Formula

a(n) = (22*n*(n - 1) - 5*(2*n - 1)*(-1)^n + 7)/4.

G.f.: x*(3 + 6*x + 26*x^2 + 6*x^3 + 3*x^4)/((1 + x)^2*(1 - x)^3).

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

a(2*n)+a(2*n+1)= 11*A000290(2*n)+6; a(2*n-1)+a(2*n) = 11*A000290(2*n-1)+1.

Extensions

Edited by N. J. A. Sloane, Jul 05 2010: offset changed to 1 (since this is a list), and terms verified.