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

Author

R. J. Mathar, Aug 16 2019

Keywords

• nonn
• easy

Links

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

Crossrefs

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

Programs

Maple

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

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