The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A106353

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A106353

Number of compositions of n into 4 parts such that no two adjacent parts are equal.
(history; published version)

#15 by Harvey P. Dale at Sun Apr 02 15:16:28 EDT 2023

STATUS

editing

approved

#14 by Harvey P. Dale at Sun Apr 02 15:16:25 EDT 2023

LINKS

<a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 0, -2, 0, 0, 1, 1, -1).

STATUS

approved

editing

#13 by Harvey P. Dale at Sun Apr 02 15:14:54 EDT 2023

STATUS

editing

approved

#12 by Harvey P. Dale at Sun Apr 02 15:14:51 EDT 2023

MATHEMATICA

Drop[CoefficientList[Series[(8x^10+4x^9+6x^8+4x^7+2x^6)/((1-x)(1-x^2)(1-x^3)(1-x^4)), {x, 0, 60}], x], 6] (* or *) LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {2, 6, 14, 24, 46, 66, 100, 138, 192, 246}, 60] (* Harvey P. Dale, Apr 02 2023 *)

STATUS

approved

editing

#11 by Alois P. Heinz at Thu Apr 28 20:22:40 EDT 2022

STATUS

editing

approved

#10 by Alois P. Heinz at Thu Apr 28 20:22:37 EDT 2022

LINKS

A. Knopfmacher and H. Prodinger, <a href="http://web.witsdx.acdoi.za/Academic/Science/Maths/Stafforg/Knopfmacher10.1006/Publicationseujc.1998.htm0216">On Carlitz compositions</a>, European Journal of Combinatorics, Vol. 19, 1998, pp. 579-589.

STATUS

approved

editing

#9 by Russ Cox at Fri Mar 30 17:37:15 EDT 2012

AUTHOR

_Christian G. Bower (bowerc(AT)usa.net), _, Apr 29 2005

Discussion

Fri Mar 30

17:37

OEIS Server: https://oeis.org/edit/global/178

#8 by Ralf Stephan at Tue Nov 16 04:24:54 EST 2010

STATUS

reviewed

approved

#7 by Klaus Brockhaus at Tue Nov 16 00:39:07 EST 2010

STATUS

proposed

reviewed

#6 by Klaus Brockhaus at Tue Nov 16 00:38:19 EST 2010

FORMULA

G.f.: (8x8*x^10+4x4*x^9+6x6*x^8+4x4*x^7+2x2*x^6) / ((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

STATUS

reviewed

proposed