A309717 Convolve Fibonacci, Pell and bronze Fibonacci numbers.

0, 0, 0, 1, 6, 28, 114, 432, 1566, 5517, 19068, 65044, 219852, 738316, 2468028, 8222805, 27330858, 90685224, 300521622, 994991716, 3292117698, 10887332473, 35992718136, 118958691528, 393093822744, 1298783453112, 4290755845176, 14174217683209, 46821054068430, 154655837126740

Offset

0,5

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (6,-8,-6,8,6,1).

Formula

G.f.: -x^3/( (x^2+2*x-1) * (x^2+3*x-1) * (x^2+x-1) ) = A006190(x) * A000045(x) * A000129(x).

Conjecture: 2*a(n) = A117936(n,3).

2*a(n) = A006190(n) + A000045(n) - 2*A000129(n). - R. J. Mathar, Mar 10 2023, typo corrected by Xiaoyuan Wang and Greg Dresden, May 08 2024

Maple

-x^3/( (x^2+2*x-1)*(x^2+3*x-1)*(x^2+x-1) ) ;
taylor(%, x=0, 30) ;
gfun[seriestolist](%) ;

Crossrefs

Cf. A006684, A006190 (bronze Fibonacci numbers), A117936.

Sequence in context: A253068 A055220 A027106 * A089096 A229587 A230492

Adjacent sequences: A309714 A309715 A309716 * A309718 A309719 A309720

Keyword

nonn,easy

Author

R. J. Mathar, Aug 16 2019

Status

approved