The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A015451 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A015451

a(n) = 6*a(n-1) + a(n-2) for n > 1, with a(0) = a(1) = 1.
(history; published version)

#70 by R. J. Mathar at Wed Feb 14 07:29:48 EST 2024

STATUS

editing

approved

#69 by R. J. Mathar at Wed Feb 14 07:29:44 EST 2024

FORMULA

a(n) = Sum_{k=0..n} A046854(n-1,k)*6^k. - R. J. Mathar, Feb 14 2024

STATUS

approved

editing

#68 by Joerg Arndt at Sat Dec 30 23:40:27 EST 2023

STATUS

editing

approved

#67 by Paolo P. Lava at Sat Dec 30 11:56:22 EST 2023

FORMULA

a(n) = (1/10)*[3 - sqrt(10)]^n*sqrt(10) - (1/10)*[3 + sqrt(10)]^n*sqrt(10) + (1/2)*[3 + sqrt(10)]^n + (1/2) *[3 - sqrt(10)]^n, with n >= 0. - Paolo P. Lava, Jun 25 2008

STATUS

approved

editing

#66 by Charles R Greathouse IV at Thu Sep 08 08:44:40 EDT 2022

PROG

(MAGMAMagma) [n le 2 select 1 else 6*Self(n-1) + Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 08 2012

Discussion

Thu Sep 08

08:44

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

#65 by Susanna Cuyler at Tue Dec 19 18:32:36 EST 2017

STATUS

proposed

approved

#64 by G. C. Greubel at Tue Dec 19 17:34:30 EST 2017

STATUS

editing

proposed

#63 by G. C. Greubel at Tue Dec 19 17:34:00 EST 2017

COMMENTS

Row m=6 of A135597.

MATHEMATICA

CoefficientList[Series[(1-5*x)/(1-6*x-x^2), {x, 0, 50}], x] (* G. C. Greubel, Dec 19 2017 *)

PROG

(PARI) x='x+O('x^30); Vec((1-5*x)/(1-6*x-x^2)) \\ G. C. Greubel, Dec 19 2017

CROSSREFS

Row m=6 of A135597.

STATUS

approved

editing

#62 by N. J. A. Sloane at Wed Jun 07 13:22:42 EDT 2017

STATUS

editing

approved

#61 by N. J. A. Sloane at Wed Jun 07 13:22:38 EDT 2017

COMMENTS

a(n+1) equals the number of sequences on over the alphabet {0,1,2,3,4,5,6} of length n such that no two consecutive terms differ by 4. - David Nacin, May 31 2017

STATUS

approved

editing