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Revision History for A212257

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A212257

Number of (v,w,x,y,z) with all terms in {0,1,...,n} and v=average(w,x,y,z).
(history; published version)

#11 by N. J. A. Sloane at Sat Sep 10 12:28:16 EDT 2016

STATUS

proposed

approved

#10 by Benedict W. J. Irwin at Mon Sep 05 10:18:34 EDT 2016

STATUS

editing

proposed

#9 by Benedict W. J. Irwin at Mon Sep 05 09:46:00 EDT 2016

LINKS

<a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,0,-4,6,-4,1)

STATUS

proposed

editing

Discussion

Mon Sep 05

09:47

Benedict W. J. Irwin: Is that the correct way to do the link?
Do I need to update the index as well or is that done automatically?

#8 by Michel Marcus at Mon Sep 05 08:52:56 EDT 2016

STATUS

editing

proposed

Discussion

Mon Sep 05

09:00

Michel Marcus: One could add a "Index entries for linear recurrences with constant coefficients," link like in say A276289

#7 by Michel Marcus at Mon Sep 05 08:52:17 EDT 2016

FORMULA

a(n) =4a 4*a(n-1)-6a6*a(n-2)+4a4*a(n-3)-4a4*a(n-5)+6a6*a(n-6)-4a4*a(n-7)+a(n-8).

a(n) = (1+7*(-1)^n)/8+n+3*n^2/2+n^3+n^4/4-sin(n*Pi/2).

MATHEMATICA

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

STATUS

proposed

editing

#6 by Benedict W. J. Irwin at Mon Sep 05 05:49:04 EDT 2016

STATUS

editing

proposed

#5 by Benedict W. J. Irwin at Mon Sep 05 05:48:17 EDT 2016

FORMULA

From Benedict W. J. Irwin, Sep 05 2016: (Start)

a(n)=(1+7*(-1)^n)/8+n+3*n^2/2+n^3+n^4/4-sin(n*Pi/2).

G.f.: 7/(8*(1+x))-x/(1+x^2)+(-1-26*x-16*x^2-6*x^3+x^4)/(8*(x-1)^5).

(End)

MATHEMATICA

Table[(1+7(-1)^n)/8+n+3n^2/2+n^3+n^4/4-Sin[n Pi/2], {n, 0, 30}] (* Benedict W. J. Irwin, Sep 05 2016 *)

STATUS

approved

editing

#4 by T. D. Noe at Wed May 30 12:58:38 EDT 2012

STATUS

proposed

approved

#3 by Clark Kimberling at Wed May 30 12:41:08 EDT 2012

STATUS

editing

proposed

#2 by Clark Kimberling at Tue May 15 15:27:29 EDT 2012

NAME

allocated for Clark KimberlingNumber of (v,w,x,y,z) with all terms in {0,1,...,n} and v=average(w,x,y,z).

DATA

1, 2, 21, 64, 157, 322, 601, 1024, 1641, 2498, 3661, 5184, 7141, 9602, 12657, 16384, 20881, 26242, 32581, 40000, 48621, 58562, 69961, 82944, 97657, 114242, 132861, 153664, 176821, 202498, 230881, 262144, 296481, 334082, 375157

OFFSET

0,2

COMMENTS

For a guide to related sequences, see A211795.

FORMULA

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

MATHEMATICA

t = Compile[{{n, _Integer}}, Module[{s = 0},

(Do[If[4 v == w + x + y + z, s = s + 1], {v, 0, #},

{w, 0, #}, {x, 0, #}, {y, 0, #}, {z, 0, #}] &[n]; s)]];

Map[t[#] &, Range[0, 40]] (* A212257 *)

(* Peter Moses, Apr 13 2012 *)

CROSSREFS

Cf. A211795.

KEYWORD

allocated

nonn

AUTHOR

Clark Kimberling, May 15 2012

STATUS

approved

editing

Discussion

Tue May 29

21:29

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A212257 and click the button that reads
"These changes are ready for review by an OEIS Editor."

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