A192251 1-sequence of reduction of central binomial coefficient sequence by x^2 -> x+1.

0, 2, 8, 48, 258, 1518, 8910, 53526, 323796, 1976876, 12138456, 74921904, 464320368, 2887660168, 18011618368, 112633305568, 705899650498, 4432668783838, 27882818399038, 175661366346838, 1108193133814138, 6999963827434378, 44265660573879298

Offset

1,2

Comments

See A192232, A192250.

Links

Table of n, a(n) for n=1..23.

Formula

a(n) = 2*A192070(n).

Conjecture: (n-1)*(n-2)*a(n) -(5*n-7)*(n-2)*a(n-1) -2*(2*n-3)*(3*n-8)*a(n-2) +4*(2*n-3)*(2*n-5)*a(n-3)=0. - R. J. Mathar, May 04 2014

a(n) = Sum_{i=0..n-1} A000045(i)*binomial(2*i, i). - John M. Campbell, Feb 01 2016

Mathematica

(See A192250.)
Table[Sum[Fibonacci[i] Binomial[2 i, i], {i, 0, n - 1}], {n, 23}] (* Michael De Vlieger, Feb 01 2016 *)

Prog

(Magma) [&+[Fibonacci(k)*Binomial(2*k, k): k in [0..n]]: n in [0..28]]; // Vincenzo Librandi, Feb 04 2016

Crossrefs

Cf. A192232, A192250, A192070.

Sequence in context: A173841 A004141 A009693 * A104190 A152661 A177066

Adjacent sequences: A192248 A192249 A192250 * A192252 A192253 A192254

Keyword

nonn

Author

Clark Kimberling, Jun 27 2011

Status

approved