The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A029549 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A029549

a(n + 3) = 35*a(n + 2) - 35*a(n + 1) + a(n), with a(0) = 0, a(1) = 6, a(2) = 210.
(history; published version)

#155 by Michael De Vlieger at Thu Sep 12 07:49:41 EDT 2024

STATUS

reviewed

approved

#154 by Joerg Arndt at Thu Sep 12 03:32:33 EDT 2024

STATUS

proposed

reviewed

#153 by Pontus von Brömssen at Wed Sep 11 14:23:44 EDT 2024

STATUS

editing

proposed

#152 by Pontus von Brömssen at Wed Sep 11 14:22:16 EDT 2024

FORMULA

a(n) = binomial(A001652A046090(n), 2) = A000217(A001652(n)). - Mitch Harris, Apr 19 2007, R. J. Mathar, Jun 26 2009

STATUS

proposed

editing

Discussion

Wed Sep 11

14:23

Pontus von Brömssen: Digging in the version history, I found a correct version of the formula by Harris/Mathar (see version #7).

#151 by Pontus von Brömssen at Wed Sep 11 12:49:38 EDT 2024

STATUS

editing

proposed

Discussion

Wed Sep 11

13:04

Pontus von Brömssen: The first formula after Gosper's formulas seems to be an incorrect version of the formula on the preceding line.

#150 by Pontus von Brömssen at Wed Sep 11 12:48:01 EDT 2024

FORMULA

a(n) = A002378(A011900(n)-1) = A002378(A053141(n)). - Pontus von Brömssen, Sep 11 2024

STATUS

proposed

editing

Discussion

Wed Sep 11

12:49

Pontus von Brömssen: I realized that my formula is almost the same as the 2nd formula from  Bill Gosper, Feb 07 2010. But maybe we can have both?

#149 by Michel Marcus at Wed Sep 11 12:25:43 EDT 2024

STATUS

editing

proposed

#148 by Michel Marcus at Wed Sep 11 12:25:38 EDT 2024

FORMULA

a(n) = ceiling((3 + 2*sqrt(2))^(2n + 1) - 6)/32 = floor((1/32) (1+sqrt(2))^(4n+2)). - Ant King , Dec 13 2010

STATUS

proposed

editing

#147 by Pontus von Brömssen at Wed Sep 11 07:51:38 EDT 2024

STATUS

editing

proposed

#146 by Pontus von Brömssen at Wed Sep 11 07:02:48 EDT 2024

DATA

0, 6, 210, 7140, 242556, 8239770, 279909630, 9508687656, 323015470680, 10973017315470, 372759573255306, 12662852473364940, 430164224521152660, 14612920781245825506, 496409142337836914550, 16863297918705209269200, 572855720093639278238256

FORMULA

a(n) = A002378(A011900(n)-1). - Pontus von Brömssen, Sep 11 2024

PROG

(Magma) R<x>:=PowerSeriesRing(Integers(), 25); [0] cat Coefficients(R!(6/(1-35*x+35*x^2-x^3))); // G. C. Greubel, Jul 15 2018

CROSSREFS

Cf. A000217, A001109, A001652, A002315, A002378, A011900, A029546, A046090, A046729, A053141, A084159, A096979, A157259, A165518.

STATUS

approved

editing