The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A094687

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A094687

Convolution of Fibonacci and Jacobsthal numbers.
(history; published version)

#26 by Charles R Greathouse IV at Thu Sep 08 08:45:13 EDT 2022

PROG

(MAGMAMagma) I:=[0, 0, 1, 2]; [n le 4 select I[n] else 2*Self(n-1) + 2*Self(n-2) -3*Self(n-3) -2*Self(n-4): n in [1..40]]; // G. C. Greubel, Mar 06 2019

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#25 by Peter Luschny at Sat Jan 04 06:10:52 EST 2020

STATUS

proposed

approved

#24 by Peter Luschny at Sat Jan 04 04:37:49 EST 2020

STATUS

editing

proposed

#23 by Peter Luschny at Sat Jan 04 04:37:34 EST 2020

MAPLE

with(combstruct):

TSU := [T, { T = Sequence(S, card > 1), S = Sequence(U, card > 0), U = Sequence(Z, card > 1)}, unlabeled]:

seq(count(TSU, size = j+2), j=0..32); # Peter Luschny, Jan 04 2020

STATUS

approved

editing

#22 by N. J. A. Sloane at Thu Apr 04 21:06:46 EDT 2019

STATUS

proposed

approved

#21 by Jon E. Schoenfield at Sat Mar 09 22:13:18 EST 2019

STATUS

editing

proposed

Discussion

Sun Mar 10

05:10

Michel Marcus: you give 2 formulas a(n) = J(n+1) - F(n+1)   and a(n) = Sum_{k=0..n} F(k)*J(n-k),

05:11

Michel Marcus: the 2nd one is already in this page : see 3rd formula

05:15

Michel Marcus: the 1st one is already in this page : see 2nd comment (but there is a difference of sign)  (it seems David Callan formula gives negative numbers)  (can someone else check what I say)

Thu Apr 04

21:06

N. J. A. Sloane: This formula, Also difference of Fibonacci and Jacobsthal numbers shifted left: a(n) = A000045(n+1) - A001045(n+1). - David Callan, Jul 22 2008, is correct!

#20 by Jon E. Schoenfield at Sat Mar 09 22:13:15 EST 2019

FORMULA

a(n) = Sum_{k=0..n} A000045(k)*A001045(n-k).

a(n) = J(n+1) - F(n+1) = Sum_{ k=0..n } F(k)*J(n-k), where J=A001045, F=A000045. - Yuchun Ji, Mar 05 2019

EXAMPLE

a(2) = 0 + 2*0 + 1 = 1

a(3) = 1 + 2*0 + 1 = 2

a(4) = 2 + 2*1 + 2 = 6

a(5) = 6 + 2*2 + 3 = 13

a(6) = 13 + 2*6 + 5 = 30

a(7) = 30 + 2*13 + 8 = 64

a(8) = 64 + 2*30 + 13 = 137

STATUS

reviewed

editing

#19 by Michael B. Porter at Fri Mar 08 02:05:08 EST 2019

STATUS

proposed

reviewed

#18 by Michel Marcus at Wed Mar 06 00:42:05 EST 2019

STATUS

editing

proposed

#17 by Michel Marcus at Wed Mar 06 00:41:55 EST 2019

FORMULA

a(n) = J(n+1)-F(n+1) = Sum_{ k=0..n } F(k)*J(n-k), where J=A001045, F=A000045. - Yuchun Ji, Mar 05 2019.

STATUS

proposed

editing

Discussion

Wed Mar 06

00:42

Michel Marcus: no period there