A063092 a(0)=1, a(1)=2 and, for n>1, a(n) = a(n-1) + 11*a(n-2).

1, 2, 13, 35, 178, 563, 2521, 8714, 36445, 132299, 533194, 1988483, 7853617, 29726930, 116116717, 443112947, 1720396834, 6594639251, 25519004425, 98060036186, 378769084861, 1457429482907, 5623889416378, 21655613728355, 83518397308513, 321730148320418

Offset: 0

Author

John W. Layman, Apr 29 2003

Keywords

• nonn

Comments

The binomial transform of this sequence is {(3^n)F(n+1)} where {F(n)} is the Fibonacci sequence A000045.

Links

• Harry J. Smith, Table of n, a(n) for n=0..200
• Index entries for linear recurrences with constant coefficients, signature (1,11).

Crossrefs

Cf. A000045.

Programs

Mathematica

LinearRecurrence[{1,11},{1,2},30] (* Harvey P. Dale, Oct 25 2020 *)

PARI

{ for (n=0, 200, if (n>1, a=a1 + 11*a2; a2=a1; a1=a, if (n, a=2; a2=1; a1=2, a=1)); write("b063092.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 18 2009

Formula

G.f.: (1+x)/(1-x-11*x^2). - Jaume Oliver Lafont, Sep 07 2009

a(n) = A015447(n) + A015447(n-1), n>0. - Ralf Stephan, Jul 21 2013

a(n)^2 - (3*A015447(n-1))^2 - (3*A015447(n-1))*a(n) = (-11)^n. - Philippe Deléham, Mar 17 2023