The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A081187

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A081187

5th binomial transform of (1,0,1,0,1,...), A059841.
(history; published version)

#42 by Michael De Vlieger at Sat Jan 13 20:32:29 EST 2024

STATUS

proposed

approved

#41 by Jon E. Schoenfield at Sat Jan 13 18:16:59 EST 2024

STATUS

editing

proposed

#40 by Jon E. Schoenfield at Sat Jan 13 18:16:57 EST 2024

COMMENTS

a(n) is also the number of words of length n over an alphabet of six letters, of which a chosen one appears an even number of times. See a comment in A007582, also for the crossrefs, for the 1- to 11- letter word cases. - Wolfdieter Lang, Jul 17 2017

FORMULA

a(n) = 10*a(n-1) - 24*a(n-2) with n > 1, a(0)=1, a(1)=5.

E.g.f.: exp(5*x)*cosh(x) = (1/2)*E(0), where E(k) = 1 +( 2^k)/(3^k - 6*x*(9^k)/(6*x*(3^k) + (k+1)*(2^k)/E(k+1))); (continued fraction). - Sergei N. Gladkovskii, Nov 21 2011

STATUS

approved

editing

#39 by Alois P. Heinz at Sat Jan 13 17:33:32 EST 2024

STATUS

reviewed

approved

#38 by Michel Marcus at Sat Jan 13 04:01:15 EST 2024

STATUS

proposed

reviewed

#37 by G. C. Greubel at Sat Jan 13 03:54:16 EST 2024

STATUS

editing

proposed

#36 by G. C. Greubel at Sat Jan 13 03:53:56 EST 2024

FORMULA

a(n) = A074612(n)/2. - G. C. Greubel, Jan 13 2024

CROSSREFS

Cf. A007582, A074612, A081189.

STATUS

approved

editing

#35 by Charles R Greathouse IV at Thu Sep 08 08:45:09 EDT 2022

PROG

(MAGMAMagma) [4^n/2 + 6^n/2: n in [0..25]]; // Vincenzo Librandi, Aug 07 2013

Discussion

Thu Sep 08

08:45

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

#34 by Susanna Cuyler at Fri Dec 27 08:56:07 EST 2019

STATUS

proposed

approved

#33 by Michel Marcus at Fri Dec 27 01:16:57 EST 2019

STATUS

editing

proposed