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A212560
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Number of (w,x,y,z) with all terms in {1,...,n} and w+x<=y+z.
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6
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0, 1, 11, 50, 150, 355, 721, 1316, 2220, 3525, 5335, 7766, 10946, 15015, 20125, 26440, 34136, 43401, 54435, 67450, 82670, 100331, 120681, 143980, 170500, 200525, 234351, 272286, 314650, 361775, 414005, 471696, 535216, 604945, 681275
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OFFSET
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0,3
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COMMENTS
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For a guide to related sequences, see A211795.
For n>=1, a(n) is the n-th antidiagonal sums of the convolution array A213831. [Clark Kimberling, Jul 04 2012]
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LINKS
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Table of n, a(n) for n=0..34.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
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a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).
a(n) = (n + 2*n^3 + 3*n^4)/6. - Clark Kimberling, Jul 10 2012
G.f.: x*(1 + x)*(1 + 5*x)/(1 - x)^5. - Clark Kimberling, Jul 10 2012
a(n) = Sum_{k=0..n} A059722(k). - J. M. Bergot, Nov 02 2012
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MATHEMATICA
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t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w + x <= y + z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212560 *)
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CROSSREFS
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Cf. A211795.
Sequence in context: A241406 A215728 A185019 * A340130 A211920 A167423
Adjacent sequences: A212557 A212558 A212559 * A212561 A212562 A212563
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, May 21 2012
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STATUS
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approved
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