The On-Line Encyclopedia of Integer Sequences (OEIS)

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A212900

Number of (w,x,y,z) with all terms in {0,...,n} and distinct consecutive gap sizes.
(history; published version)

#12 by Alois P. Heinz at Tue May 07 18:33:02 EDT 2019

STATUS

proposed

approved

#11 by Sean A. Irvine at Tue May 07 18:26:32 EDT 2019

STATUS

editing

proposed

#10 by Sean A. Irvine at Tue May 07 18:26:16 EDT 2019

NAME

Number of (w,x,y,z) with all terms in {0,...,n} and distinct consecutive gapsizesgap sizes.

COMMENTS

The gapsizes gap sizes are |w-x|, |x-y|, |y-z|. Every term is even.

STATUS

approved

editing

#9 by Charles R Greathouse IV at Sat Jun 13 00:54:14 EDT 2015

LINKS

<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (2,1,-3,-1,1,3,-1,-2,1).

Discussion

Sat Jun 13

00:54

OEIS Server: https://oeis.org/edit/global/2439

#8 by Charles R Greathouse IV at Fri Jun 12 15:33:21 EDT 2015

LINKS

<a href="/index/Rec#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (2,1,-3,-1,1,3,-1,-2,1).

Discussion

Fri Jun 12

15:33

OEIS Server: https://oeis.org/edit/global/2437

#7 by Harvey P. Dale at Sun Aug 25 16:33:14 EDT 2013

STATUS

editing

approved

#6 by Harvey P. Dale at Sun Aug 25 16:33:09 EDT 2013

MATHEMATICA

LinearRecurrence[{2, 1, -3, -1, 1, 3, -1, -2, 1}, {0, 4, 28, 122, 340, 786, 1558, 2814, 4690}, 40] (* Harvey P. Dale, Aug 25 2013 *)

STATUS

approved

editing

#5 by T. D. Noe at Tue Jun 12 17:22:11 EDT 2012

STATUS

proposed

approved

#4 by Clark Kimberling at Mon Jun 11 12:54:11 EDT 2012

STATUS

editing

proposed

#3 by Clark Kimberling at Mon Jun 11 12:36:22 EDT 2012

COMMENTS

The gapsizes are |w-x|, |x-y|, |y-z|. Every term is even. For a guide to related sequences, see A211795.

For a guide to related sequences, see A211795.

LINKS

<a href="/index/Rec#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (2,1,-3,-1,1,3,-1,-2,1).

FORMULA

a(n) = 2*a(n-1)+a(n-2)-3*a(n-3)-a(n-4)+a(n-5)+3*a(n-6)-a(n-7)-2a2*a(n-8)+a(n-9).

G.f.: f(x)/g(x), where f(x) = 2(2*x + 10*x^2 + 31*x^3 + 40*x^4 + 36*x^5 + 18*x^6 + 7*x^7) and g(x)=((1-x)^5)((1+x)^2)(1+x+x^2).