A179339 Positive integers of the form (30*m^2+1)/11.

11, 221, 461, 1091, 1571, 2621, 3341, 4811, 5771, 7661, 8861, 11171, 12611, 15341, 17021, 20171, 22091, 25661, 27821, 31811, 34211, 38621, 41261, 46091, 48971, 54221, 57341, 63011, 66371, 72461, 76061, 82571, 86411, 93341, 97421

Offset: 1

Author

Bruno Berselli, Jul 11 2010 - Dec 10 2010

Keywords

• nonn
• easy

Comments

Here m = (11*(2*n-1)+3*(-1)^n)/4 for n>0.

More generally, (t*((11*(2*n-1)+k*(-1)^n)/4)^2 +1)/11 = ( 22*t*n*(n-1) +t*k*(2*n-1)*(-1)^n+(t*(k^2+121)+16)/22 )/8 for any natural number t == 2, 6, 7, 8, 10 (mod 11) and k = -5, -1, -9, 3, 7, respectively.

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, A179338, A179370.

Programs

Mathematica

LinearRecurrence[{1,2,-2,-1,1},{11,221,461,1091,1571},40] (* Harvey P. Dale, Mar 03 2023 *)

Formula

a(n) = (330*n*(n-1)+45*(2*n-1)*(-1)^n+89)/4.

G.f.: x*(11+210*x+218*x^2+210*x^3+11*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).