The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A116593 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A116593

a(n) = b(n+2) + b(n), where b(n) = A006046(n) is the sequence defined by b(0)=0, b(1)=1, b(n) = 2*b((n-1)/2) + b((n+1)/2) for n =3,5,7,... and b(n) = 3*b(n/2) for n =2,4,6,....
(history; published version)

#12 by Joerg Arndt at Wed Dec 13 02:45:11 EST 2017

STATUS

proposed

approved

#11 by Michel Marcus at Wed Dec 13 02:35:18 EST 2017

STATUS

editing

proposed

#10 by Michel Marcus at Wed Dec 13 02:35:13 EST 2017

CROSSREFS

Cf. A000030, A000032, A084230.

STATUS

approved

editing

#9 by Paul D. Hanna at Sat Oct 28 10:49:07 EDT 2017

STATUS

reviewed

approved

#8 by Michel Marcus at Sat Oct 28 02:28:06 EDT 2017

STATUS

proposed

reviewed

#7 by G. C. Greubel at Sat Oct 28 01:40:16 EDT 2017

STATUS

editing

proposed

#6 by G. C. Greubel at Fri Oct 27 23:09:28 EDT 2017

NAME

a(n) = b(n+2) + b(n), where b(n) = A006046(n) is the sequence defined by b(0)=0, b(1)=1, b(n) =2b 2*b((n-1)/2) + b((n+1)/2) for n =3,5,7,... and b(n) =3b 3*b(n/2) for n =2,4,6,....

LINKS

G. C. Greubel, <a href="/A116593/b116593.txt">Table of n, a(n) for n = 0..5000</a>

FORMULA

b[0] := 0 b[1] := 1 b[n_?EvenQ] := b[n] = 3*b[n/2] b[n_?OddQ] := b[n] = 2*b[(n - 1)/2] + b[(n + 1)/2] a(n) = b[n-1]+b[n+1]

a(n) = A006046(n+2) + A006046(n) for n>=1.

MATHEMATICA

b[0] := 0 b[1] := 1 ; b[n_?EvenQ] := b[n] = 3*b[n/2] ; b[n_?OddQ] := b[n] = 2*b[(n - 1)/2] + b[(n + 1)/2] ; L[0] = 1; L[n_] := L[n] = b[n - 1] + b[n + 1] a = ; Table[L[n], {n, 1, 200}]

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 17:34:20 EDT 2012

AUTHOR

_Roger L. Bagula (rlbagulatftn(AT)yahoo.com), _, Mar 27 2006

Discussion

Fri Mar 30

17:34

OEIS Server: https://oeis.org/edit/global/158

#4 by Russ Cox at Fri Mar 30 16:50:24 EDT 2012

EXTENSIONS

Edited by _N. J. A. Sloane (njas(AT)research.att.com), _, Apr 15 2006

Discussion

Fri Mar 30

16:50

OEIS Server: https://oeis.org/edit/global/110

#3 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

NAME

a(n)=b(n+2)+b(n), where b(n)=A006046(n) is the sequence defined by b(0)=0, b(1)=1, b(n)=2b((n-1)/2)+b((n+1)/2) for n =3,5,7,..., and b(n)=3b(n/2) for n =2,4,6,....

KEYWORD

nonn,new

nonn

EXTENSIONS

Edited by N. J. A. Sloane (njas, (AT)research.att.com), Apr 15 2006