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A185730
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Array by antidiagonals: T(n,k)=k(k+1)n(n+1)(kn-n+2k+7)/36.
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1
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1, 4, 3, 10, 13, 6, 20, 34, 28, 10, 35, 70, 76, 50, 15, 56, 125, 160, 140, 80, 21, 84, 203, 290, 300, 230, 119, 28, 120, 308, 476, 550, 500, 350, 168, 36, 165, 444, 728, 910, 925, 770, 504, 228, 45, 220, 615, 1056, 1400, 1540, 1435, 1120, 696, 300, 55, 286, 825, 1470, 2040, 2380, 2401, 2100, 1560, 930, 385, 66, 364, 1078, 1980, 2850, 3480, 3724, 3528, 2940
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OFFSET
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1,2
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COMMENTS
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This array is a member of a chain of arrays; it is the accumulation array of the array obtain by writing A125764 rectangularly -
1...3....6....10...
2...7....15...26...
3...12...27...48...
and it is the weight array of A185731. (Weight and accumulation arrays are defined at A144112.)
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LINKS
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Table of n, a(n) for n=1..74.
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FORMULA
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T(n,k)=k(k+1)n(n+1)(kn-n+2k+7)/36.
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EXAMPLE
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Northwest corner:
1....4....10....20....35
3....13...34....70....125
6....28...76....160...290
10...50...140...300...550
15...80...230...500...925
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MATHEMATICA
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f[n_, k_]:=k(1+k)n(1+n)(7+2k-n+k*n)/36;
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]]
Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
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CROSSREFS
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Cf. A144112, A125764, A185731.
Sequence in context: A081617 A103252 A065763 * A205965 A222510 A100492
Adjacent sequences: A185727 A185728 A185729 * A185731 A185732 A185733
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Feb 01 2011
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STATUS
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approved
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