Revision History for A212516
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#10 by Vaclav Kotesovec at Fri Dec 11 12:49:56 EST 2015
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#9 by Vaclav Kotesovec at Fri Dec 11 12:49:15 EST 2015
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| MATHEMATICA
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t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w > 2 x && y < 3 z, s = s + 1], {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]]; Map[t[#] &, Range[0}, , 50]] (* A212516 *)
(Do[If[w > 2 x && y < 3 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
MapTable[-n^2/24 - n^3/6 + 5*n^4/24 - 1/12*Floor[n/6] + (n/6 - n^2/12)*Floor[t[#] &, Rangen/3] - (n/12 + 5*n^2/12)*Floor[n/2] + 1/12*Floor[(1 + n)/6] + (-n/6 + n^2/12) * Floor[(1 + n)/3], {n, 0, 50]] (* A212516}] (* _Vaclav Kotesovec_, Dec 11 2015 *)
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| STATUS
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approved
editing
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#8 by Alois P. Heinz at Fri Dec 11 12:46:45 EST 2015
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#7 by Michel Marcus at Fri Dec 11 12:26:01 EST 2015
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#6 by Colin Barker at Fri Dec 11 12:10:15 EST 2015
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#5 by Colin Barker at Fri Dec 11 12:08:56 EST 2015
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| DATA
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0, 0, 0, 8, 28, 88, 186, 378, 660, 1104, 1700, 2575, 3660, 5148, 6972, 9310, 12096, 15616, 19656, 24624, 30330, 37100, 44770, 53845, 63888, 75600, 88608, 103428, 119756, 138376, 158550, 181350, 206160, 233728, 263568, 296803, 332316, 371628, 413820, 459914
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| LINKS
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Colin Barker, <a href="/A212516/b212516.txt">Table of n, a(n) for n = 0..1000</a>
<a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,-1,-4,0,2,0,-2,0,4,1,-2,-2,0,1).
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| FORMULA
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a(n)=2a) = 2*a(n-2)+2a2*a(n-3)-a(n-4)-4a4*a(n-5)+2a2*a(n-7)-2a2*a(n-9)+4a4*a(n-11)+ a(n-12)-2a2*a(n-13)-2a2*a(n-14)+a(n-16).
G.f.: x^3*(8 +28*x +72*x^2 +114*x^3 +154*x^4 +172*x^5 +176*x^6 +146*x^7 +113*x^8 +64*x^9 +26*x^10 +6*x^11 +x^12) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - Colin Barker, Dec 11 2015
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| PROG
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(PARI) concat(vector(3), Vec(x^3*(8 +28*x +72*x^2 +114*x^3 +154*x^4 +172*x^5 +176*x^6 +146*x^7 +113*x^8 +64*x^9 +26*x^10 +6*x^11 +x^12) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^100))) \\ Colin Barker, Dec 11 2015
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| KEYWORD
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nonn,easy
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| STATUS
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approved
editing
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#4 by T. D. Noe at Sat Jun 02 20:22:15 EDT 2012
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#3 by Clark Kimberling at Sat Jun 02 11:50:18 EDT 2012
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#2 by Clark Kimberling at Sun May 20 17:17:31 EDT 2012
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| NAME
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allocatedNumber of (w,x,y,z) with all terms in {1,...,n} and forw>2x Clarkand Kimberlingy<3z.
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| DATA
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0, 0, 0, 8, 28, 88, 186, 378, 660, 1104, 1700, 2575, 3660, 5148, 6972, 9310, 12096, 15616, 19656, 24624, 30330, 37100, 44770, 53845, 63888, 75600, 88608, 103428, 119756, 138376, 158550, 181350, 206160, 233728, 263568, 296803, 332316
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| OFFSET
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0,4
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| COMMENTS
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For a guide to related sequences, see A211795.
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| FORMULA
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a(n)=2a(n-2)+2a(n-3)-a(n-4)-4a(n-5)+2a(n-7)-2a(n-9)+4a(n-11)+ a(n-12)-2a(n-13)-2a(n-14)+a(n-16).
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| MATHEMATICA
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t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w > 2 x && y < 3 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212516 *)
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| CROSSREFS
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Cf. A211795, A212508.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Clark Kimberling, May 20 2012
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| STATUS
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approved
editing
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Discussion
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| Sun May 27
| 20:04
| 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/A212516 and click the button that reads
"These changes are ready for review by an OEIS Editor."
Thanks.
- The OEIS Server
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#1 by Clark Kimberling at Sat May 19 19:57:33 EDT 2012
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| NAME
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allocated for Clark Kimberling
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| KEYWORD
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allocated
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| STATUS
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approved
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