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A132121
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Triangle read by rows: T(n,k)=n*(n+1)*((3*k+2)*n+1)/6, 0<=k<=n.
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8
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0, 1, 2, 5, 11, 17, 14, 32, 50, 68, 30, 70, 110, 150, 190, 55, 130, 205, 280, 355, 430, 91, 217, 343, 469, 595, 721, 847, 140, 336, 532, 728, 924, 1120, 1316, 1512, 204, 492, 780, 1068, 1356, 1644, 1932, 2220, 2508, 285, 690, 1095, 1500, 1905, 2310, 2715, 3120
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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G.f.: Sum_{n>=0} Sum_{k>=0} T(n,k)*x^n*y^k = x*(x*y+1+x)/((1-x)^4*(1-y)^2). - R. J. Mathar, Jul 28 2016. Note that this generates a full array, not just the triangular subspace.
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EXAMPLE
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0;
1, 2;
5, 11, 17;
14, 32, 50, 68;
30, 70, 110, 150, 190;
55, 130, 205, 280, 355, 430;
91, 217, 343, 469, 595, 721, 847;
140, 336, 532, 728, 924, 1120, 1316, 1512;
204, 492, 780, 1068, 1356, 1644, 1932, 2220, 2508;
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MAPLE
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n*(n+1)*((3*k+2)*n+1)/6 ;
end proc:
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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