The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A212503 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A212503

Number of (w,x,y,z) with all terms in {1,...,n} and w<2x and y<2z.
(history; published version)

#12 by Harvey P. Dale at Wed Jun 14 14:02:03 EDT 2017

STATUS

editing

approved

#11 by Harvey P. Dale at Wed Jun 14 14:02:00 EDT 2017

MATHEMATICA

LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {0, 1, 9, 49, 144, 361, 729, 1369}, 40] (* Harvey P. Dale, Jun 14 2017 *)

STATUS

approved

editing

#10 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 (2,2,-6,0,6,-2,-2,1).

Discussion

Sat Jun 13

00:54

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

#9 by Charles R Greathouse IV at Fri Jun 12 15:33:20 EDT 2015

LINKS

<a href="/index/Rec#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).

Discussion

Fri Jun 12

15:33

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

#8 by Bruno Berselli at Thu May 31 17:14:51 EDT 2012

STATUS

editing

approved

#7 by Bruno Berselli at Thu May 31 17:14:21 EDT 2012

LINKS

<a href="/index/Rec#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).

FORMULA

a(n) = (A077043(n))^2.

a(n) =2a 2*a(n-1)+2a2*a(n-2)-6a6*a(n-3)+6a6*a(n-5)-2a2*a(n-6)-2a2*a(n-7)+a(n-8).

G.f.: x*(1+x+x^2)*(1+6*x+22*x^2+6*x^3+x^4)/((1+x)^3*(1-x)^5). [Bruno Berselli, May 31 2012]

STATUS

approved

editing

#6 by T. D. Noe at Thu May 31 13:04:58 EDT 2012

STATUS

proposed

approved

#5 by Clark Kimberling at Thu May 31 12:03:59 EDT 2012

STATUS

editing

proposed

#4 by Clark Kimberling at Thu May 31 10:26:40 EDT 2012

KEYWORD

nonn,changed,easy

Discussion

Thu May 31

10:29

Clark Kimberling: Bruno - Mathematica "gives up" when FindGeneratingFunction is added.  For shorter recurrences, FindGeneratingFunction works fine.  For sequences higher than A212503 I'll include g.f. unless Mathematica "gives up".

#3 by Clark Kimberling at Sat May 19 20:09:53 EDT 2012

NAME

allocated for Clark KimberlingNumber of (w,x,y,z) with all terms in {1,...,n} and w<2x and y<2z.

DATA

0, 1, 9, 49, 144, 361, 729, 1369, 2304, 3721, 5625, 8281, 11664, 16129, 21609, 28561, 36864, 47089, 59049, 73441, 90000, 109561, 131769, 157609, 186624, 219961, 257049, 299209, 345744, 398161, 455625, 519841, 589824, 667489, 751689

OFFSET

0,3

COMMENTS

For a guide to related sequences, see A211795.

FORMULA

a(n)=(A077043(n))^2.

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

MATHEMATICA

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

(Do[If[w < 2 x && y < 2 z, s = s + 1],

{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];

Map[t[#] &, Range[0, 40]] (* A212503 *)

CROSSREFS

Cf. A211795.

KEYWORD

allocated

nonn

AUTHOR

Clark Kimberling, May 19 2012

STATUS

approved

editing

Discussion

Sun May 27

07:45

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/A212503 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

Thu May 31

03:03

Bruno Berselli: Clark, can you add the g.f.? Thanks ;)

03:06

Bruno Berselli: Also "easy" in keyword (it is sequence with linear recurrence). Thanks!