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

1,3

Links

Table of n, a(n) for n=1..26.

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

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]

Mathematica

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

Crossrefs

Cf. A000045, A041059.

Sequence in context: A254600 A354906 A060499 * A060498 A274119 A171316

Adjacent sequences: A164825 A164826 A164827 * A164829 A164830 A164831

Keyword

nonn,easy

Author

Mark Dols, Aug 27 2009

Status

approved