The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A160156 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A160156

Partial sums of A007583.
(history; published version)

#39 by Alois P. Heinz at Tue Oct 18 03:31:22 EDT 2022

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proposed

approved

#38 by Michel Marcus at Tue Oct 18 02:48:06 EDT 2022

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editing

proposed

#37 by Michel Marcus at Tue Oct 18 02:48:02 EDT 2022

LINKS

Hacène Belbachir and El-Mehdi Mehiri, <a href="https://arxiv.org/abs/2210.08657">Enumerating moves in the optimal solution of the Tower of Hanoi</a>, arXiv:2210.08657 [math.CO], 2022.

<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,4).

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approved

editing

#36 by Michael Somos at Fri Oct 16 16:57:48 EDT 2020

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editing

approved

#35 by Michael Somos at Fri Oct 16 16:57:38 EDT 2020

FORMULA

a(n) = A034299(2*n). - Michael Somos, Oct 16 2020

EXAMPLE

G.f. = 1 + 4*x + 15*x^2 + 58*x^3 + 229*x^4 + 912*x^5 + 3643*x^6 + ... - Michael Somos, Oct 16 2020

PROG

(PARI) {a(n) = (2^(2*n + 3) + 3*n + 1)/9}; /* Michael Somos, Oct 16 2020 */

CROSSREFS

Cf. A002450, A007583, A034299, A139250.

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approved

editing

Discussion

Fri Oct 16

16:57

Michael Somos: Added more info.

#34 by Harvey P. Dale at Thu Oct 04 18:33:48 EDT 2018

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editing

approved

#33 by Harvey P. Dale at Thu Oct 04 18:33:45 EDT 2018

MATHEMATICA

LinearRecurrence[{6, -9, 4}, {1, 4, 15}, 30] (* Harvey P. Dale, Oct 04 2018 *)

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approved

editing

#32 by Susanna Cuyler at Sat Sep 01 21:30:51 EDT 2018

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proposed

approved

#31 by Jon E. Schoenfield at Sat Sep 01 18:01:59 EDT 2018

STATUS

editing

proposed

#30 by Jon E. Schoenfield at Sat Sep 01 18:01:53 EDT 2018

COMMENTS

This is the sequence A(1,4;5,-4;-1,n) of the family of sequences [a,b:c,d:k] considered by G. _Gary Detlefs, _, and treated as A(a,b;c,d;k) in the W. Lang's link given below. [_- _Wolfdieter Lang_, Nov 16 2013]

FORMULA

a(n) =[ (3n + 1 + 2^(2n+3)])/9. [From _- _Emeric Deutsch_, Jun 20 2009]

G.f. : ( -1+2*x ) / ( (-1+4*x)*(x-1)^2 ). - R. J. Mathar, Jun 28 2012

From Wolfdieter Lang, Nov 16 2013 : (Start)

MAPLE

a := proc (n) options operator, arrow: (1/3)*n+1/9+(1/9)*2^(2*n+3) end proc: seq(a(n), n = 0 .. 25); [From _# _Emeric Deutsch_, Jun 20 2009]

STATUS

approved

editing