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A309717
Convolve Fibonacci, Pell and bronze Fibonacci numbers.
1
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
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
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Aug 16 2019
STATUS
approved