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A063092
a(0)=1, a(1)=2 and, for n>1, a(n) = a(n-1) + 11*a(n-2).
4
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
0,2
COMMENTS
The binomial transform of this sequence is {(3^n)F(n+1)} where {F(n)} is the Fibonacci sequence A000045.
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
MATHEMATICA
LinearRecurrence[{1, 11}, {1, 2}, 30] (* Harvey P. Dale, Oct 25 2020 *)
PROG
(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
CROSSREFS
Cf. A000045.
Sequence in context: A254965 A038501 A009350 * A338222 A034011 A085497
KEYWORD
nonn
AUTHOR
John W. Layman, Apr 29 2003
STATUS
approved