A219314 Composition of the inverse binomial transform of Fibonacci numbers and the Catalan transform of Fibonacci numbers.

0, 1, 0, 3, 3, 13, 26, 77, 192, 529, 1412, 3873, 10603, 29315, 81318, 226763, 634627, 1782637, 5022840, 14193457, 40211105, 114191159, 324981030, 926720807, 2647513282, 7576475383, 21716189676, 62336237007, 179182653117, 515717424109, 1486119467026

Offset

0,4

Links

Fung Lam, Table of n, a(n) for n = 0..2000

Paul Barry, A Catalan transform and related transformations on integer sequences, pp. 20-22.

S. B. Ekhad and M. Yang, Proofs of Linear Recurrences of Coefficients of Certain Algebraic Formal Power Series Conjectured in the On-Line Encyclopedia Of Integer Sequences, (2017).

Formula

G.f.: ((1+2*x)*sqrt(1-2*x-3*x^2) - 1 + x + 2*x^2)/(2*(1+x)*(1-2*x-4*x^2)).

Asymptotics: a(n) ~ 3^(n+2)*5/(8*sqrt(3*Pi*n^3)). - Fung Lam, Apr 07 2014

Conjecture: n*a(n) -2*n*a(n-1) +11*(-n+2)*a(n-2) +4*(2*n-5)*a(n-3) +8*(5*n-17)*a(n-4) +24*(n-4)*a(n-5)=0. - R. J. Mathar, Jun 14 2016

Conjecture: n*(5*n-7)*a(n) -4*(5*n^2-12*n+6)*a(n-1) -(15*n^2-11*n-30) *a(n-2) +2*(35*n^2-119*n+66)*a(n-3) +12*(n-3)*(5*n2)*a(n-4)=0. - R. J. Mathar, Jun 14 2016

Crossrefs

Cf. A000045, A219312.

Sequence in context: A072552 A217246 A186743 * A288146 A019154 A255675

Adjacent sequences: A219311 A219312 A219313 * A219315 A219316 A219317

Keyword

easy,nonn

Author

Arkadiusz Wesolowski, Nov 17 2012

Status

approved