A189734 a(1)=2, a(2)=5, a(n)=2*a(n-1) + 5*a(n-2).

2, 5, 20, 65, 230, 785, 2720, 9365, 32330, 111485, 384620, 1326665, 4576430, 15786185, 54454520, 187839965, 647952530, 2235104885, 7709972420, 26595469265, 91740800630, 316458947585, 1091621898320, 3765538534565, 12989186560730, 44806065794285

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..100

Index entries for linear recurrences with constant coefficients, signature (2,5).

Formula

G.f.: x*(2+x)/(1-2*x-5*x^2). - Bruno Berselli, May 24 2011

Mathematica

LinearRecurrence[{2, 5}, {2, 5}, 40]

Prog

(Maxima) a[1]:2$ a[2]:5$ a[n]:=2*a[n-1]+5*a[n-2]$ makelist(a[n], n, 1, 26); /* Bruno Berselli, May 24 2011 */
(PARI) a(n)=([0, 1; 5, 2]^(n-1)*[2; 5])[1, 1] \\ Charles R Greathouse IV, Apr 29 2026

Crossrefs

Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189732, A189735, A189736, A189737, A189738, A189739, A189741, A189742, A189743, A189744, A189745, A189746, A189747, A189748, A189749.

Sequence in context: A124264 A274239 A271858 * A221678 A297350 A387689

Adjacent sequences: A189731 A189732 A189733 * A189735 A189736 A189737

Keyword

nonn,easy

Author

Harvey P. Dale, Apr 26 2011

Status

approved