A179338 Positive integers of the form (10*m^2+1)/11.

1, 91, 131, 401, 481, 931, 1051, 1681, 1841, 2651, 2851, 3841, 4081, 5251, 5531, 6881, 7201, 8731, 9091, 10801, 11201, 13091, 13531, 15601, 16081, 18331, 18851, 21281, 21841, 24451, 25051, 27841, 28481, 31451, 32131, 35281, 36001, 39331

Offset: 1

Author

Bruno Berselli, Jul 11 2010

Keywords

• nonn
• easy

Comments

Here m=(11*(2*n-1)+7*(-1)^n)/4 for n>0.

Links

• B. Berselli, Table of n, a(n) for n = 1..10000.
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A113338, A179088, A179337, A179339, A179370.

Programs

Magma

[(110*n*(n-1)+35*(2*n-1)*(-1)^n+39)/4: n in [1..50]]; // Vincenzo Librandi, Jul 10 2014

Mathematica

Select[(10Range[300]^2+1)/11,IntegerQ] (* or *) LinearRecurrence[ {1,2,-2,-1,1},{1,91,131,401,481},50] (* Harvey P. Dale, Jul 10 2014 *)

PARI

isok(n) = (((11*n-1) % 10 == 0) && issquare((11*n-1)/10)) \\ Michel Marcus, Jun 07 2013

Formula

a(n) = (110*n*(n-1)+35*(2*n-1)*(-1)^n+39)/4.

G.f.: x*(1+90*x+38*x^2+90*x^3+1*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).