A164828 Generalized Fibonacci numbers.

1, 1, 11, 120, 122, 1331, 1462, 15960, 17413, 190081, 207503, 2265120, 2472614, 26991251, 29463874, 321630000, 351093865, 3832568641, 4183662515, 45669193800, 49852856306, 544197756851, 594050613166, 6484703888520, 7078754501677, 77272248905281

Offset: 1

Author

Mark Dols, Aug 27 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,11,0,11,0,-1).

Crossrefs

Cf. A000045, A041059.

Programs

Mathematica

LinearRecurrence[{0,11,0,11,0,-1},{1,1,11,120,122,1331},30] (* Harvey P. Dale, Jun 14 2014 *)

Formula

For n odd a(n) = 11a(n-2) + a(n-3), for n even a(n) = 11a(n-1)- a(n-3); with a(1,2) = 1 (For Fibonacci sequence: factor 2 instead of 11).

G.f.: x*(1+x+109*x^3-10*x^4)/((1+x^2)*(1-12*x^2+x^4)). [Colin Barker, Jul 27 2012]