The On-Line Encyclopedia of Integer Sequences (OEIS)

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A212088

Number of (w,x,y,z) with all terms in {1,...,n} and w<average{x,y,z}.
(history; published version)

#19 by N. J. A. Sloane at Sun Dec 04 19:46:29 EST 2016

MATHEMATICA

(* _Peter J. C. Moses, _, Apr 13 2012 *)

Discussion

Sun Dec 04

19:46

OEIS Server: https://oeis.org/edit/global/2576

#18 by Ray Chandler at Sun Aug 02 17:55:44 EDT 2015

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editing

approved

#17 by Ray Chandler at Sun Aug 02 17:55:39 EDT 2015

LINKS

<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 5, -5, 6, -4, 1).

MATHEMATICA

LinearRecurrence[{4, -6, 5, -5, 6, -4, 1}, {0, 0, 7, 36, 117, 292, 612}, 35] (* Ray Chandler, Aug 02 2015 *)

STATUS

approved

editing

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

LINKS

<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (4,-6,5,-5,6,-4,1).

Discussion

Sat Jun 13

00:54

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

#15 by Charles R Greathouse IV at Sat Jun 13 00:28:08 EDT 2015

LINKS

<a href="/index/Rec">Index entries for to sequences related to with linear recurrences with constant coefficients</a>, signature (4,-6,5,-5,6,-4,1).

Discussion

Sat Jun 13

00:28

OEIS Server: https://oeis.org/edit/global/2438

#14 by Charles R Greathouse IV at Fri Jun 12 15:28:04 EDT 2015

LINKS

<a href="/index/Rea#recLCCRec">Index entries for sequences related to linear recurrences with constant coefficients</a>, signature (4,-6,5,-5,6,-4,1).

Discussion

Fri Jun 12

15:28

OEIS Server: https://oeis.org/edit/global/2436

#13 by Bruno Berselli at Tue Jun 05 11:51:35 EDT 2012

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editing

approved

#12 by Bruno Berselli at Tue Jun 05 11:50:51 EDT 2012

COMMENTS

Also, number of (w,x,y,z) with all terms in {1,...,n} and w>average{x,y,z}. A212088(n) + A212089(n) = n^4. For a guide to related sequences, see A211795.

a(n) + A212089(n) = n^4.

For a guide to related sequences, see A211795.

FORMULA

a(n) = 4a4*a(n-1)-6a6*a(n-2)+5a5*a(n-3)-5a5*a(n-4)+6a6*a(n-5)-4a4*a(n-6)+a(n-7).

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approved

editing

#11 by Bruno Berselli at Tue Jun 05 11:47:21 EDT 2012

STATUS

editing

approved

#10 by Bruno Berselli at Tue Jun 05 11:47:12 EDT 2012

FORMULA

G.f.: x^2*(x^4+5*x^3+15*x^2+8*x+7) / ((x^2+x+1)*(1-x)^5). - _Alois P. Heinz_, May 18 2012

KEYWORD

nonn,easy

STATUS

approved

editing