The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A001045

(Bold, blue-underlined text is an ; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

Jacobsthal sequence (or Jacobsthal numbers): a(n) = a(n-1) + 2*a(n-2), with a(0) = 0, a(1) = 1; also a(n) = nearest integer to 2^n/3.
(history; published version)

#1211 by N. J. A. Sloane at Sun Sep 22 18:42:10 EDT 2024

STATUS

proposed

#1210 by Gregory L. Simay at Mon Sep 02 00:44:50 EDT 2024

STATUS

editing

#1209 by Gregory L. Simay at Mon Sep 02 00:44:06 EDT 2024

FORMULA

a(n) = Sum_{r>=0} F(n-2r, r), where F(n, 0) is the nth Fibonacci number and F(n,r) = Sum_{j=1 to n} F(n+1-j, r-1) F(j, r-1). - _Gregory Simay_, Aug 31 2024

#1208 by Michel Marcus at Mon Sep 02 00:29:45 EDT 2024

STATUS

proposed

#1207 by Gregory L. Simay at Sun Sep 01 17:46:48 EDT 2024

STATUS

editing

Discussion

Mon Sep 02

00:25

Michel Marcus: your signature name is not correct ...

00:25

Michel Marcus: nth should be n-th

00:29

Michel Marcus: Sum_{j=1 to n} should be Sum_{j=1..n}

#1206 by Gregory L. Simay at Sun Sep 01 17:45:51 EDT 2024

FORMULA

a(n) = Sum_{j>=0} F(n-2j, j), where F(n, j) is the jth convolution of the nth Fibonacci number, defined to be F(n,0). - _Gregory Simay_, Aug 31 2024

#1205 by Joerg Arndt at Sun Sep 01 02:17:16 EDT 2024

STATUS

proposed

#1204 by Gregory L. Simay at Sat Aug 31 22:17:41 EDT 2024

STATUS

editing

Discussion

Sun Sep 01

02:17

Joerg Arndt: "convolution of the nth Fibonacci number" the operands of a convolution are sequences, not numbers. Also, there are (at least) two operands.

#1203 by Gregory L. Simay at Sat Aug 31 22:13:18 EDT 2024

FORMULA

STATUS

approved

Discussion

Sat Aug 31

22:16

Gregory L. Simay: If u=1/(1-x-x^2), then the g.f. for a(n) is easily derived from the sum,
u + x^2 u^2 + x^4 u^3 +... = u/(1-x^2 u) = 1-x -2x^2

#1202 by R. J. Mathar at Sun Aug 18 09:07:00 EDT 2024

STATUS

editing