The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A219462 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A219462

a(n) = Sum_{k = 1..2*n} binomial(2*n,k) * Fibonacci(2*k).
(history; published version)

#21 by Alois P. Heinz at Thu Oct 19 16:59:08 EDT 2023

STATUS

proposed

approved

#20 by Stefano Spezia at Thu Oct 19 15:22:18 EDT 2023

STATUS

editing

proposed

#19 by Stefano Spezia at Thu Oct 19 15:19:25 EDT 2023

FORMULA

E.g.f.: 2*exp(15*x/2)*sinh(5*sqrt(5)*x/2)/sqrt(5). - Stefano Spezia, Oct 19 2023

Discussion

Thu Oct 19

15:20

Stefano Spezia: Deleted “Empirical” from Colin g.f. since it is easy to prove that derives from the above  formula

#18 by Stefano Spezia at Thu Oct 19 15:17:24 EDT 2023

LINKS

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (15,-25).

FORMULA

Empirical G.f.: 5*x/(25*x^2-15*x+1). [_- _Colin Barker_, Dec 03 2012]

KEYWORD

nonn,easy

STATUS

approved

editing

#17 by Alois P. Heinz at Wed Jan 26 12:13:41 EST 2022

STATUS

proposed

approved

#16 by Michel Marcus at Wed Jan 26 12:11:47 EST 2022

STATUS

editing

proposed

#15 by Michel Marcus at Wed Jan 26 12:11:39 EST 2022

NAME

a(n) = Sum_{k = 1..2*n} binomial(2*n,k) * Fibonacci(2*k).

COMMENTS

a(n) = sum (A034870(n,k)*A001906(k): k=1..n).

FORMULA

a(n) = Sum_{k=1..n} A034870(n,k)*A001906(k).

PROG

(PARI) a(n) = sum(k = 1, 2*n, binomial(2*n, k) * fibonacci(2*k)); \\ Michel Marcus, Jan 26 2022

STATUS

approved

editing

#14 by Harvey P. Dale at Sat Aug 26 12:27:51 EDT 2017

STATUS

editing

approved

#13 by Harvey P. Dale at Sat Aug 26 12:27:46 EDT 2017

MATHEMATICA

Table[Sum[Binomial[2n, k]Fibonacci[2k], {k, 2n}], {n, 0, 20}] (* Harvey P. Dale, Aug 26 2017 *)

STATUS

approved

editing

#12 by Charles R Greathouse IV at Sat Jul 13 12:04:33 EDT 2013

LINKS

_Reinhard Zumkeller_, , <a href="/A219462/b219462.txt">Table of n, a(n) for n = 0..500</a>

Discussion

Sat Jul 13

12:04

OEIS Server: https://oeis.org/edit/global/1934