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A107984
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Triangle read by rows: T(n,k) = (k+1)*(n+2)*(2n-k+3)*(n-k+1)/6 for 0 <= k <= n.
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2
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1, 5, 4, 14, 16, 10, 30, 40, 35, 20, 55, 80, 81, 64, 35, 91, 140, 154, 140, 105, 56, 140, 224, 260, 256, 220, 160, 84, 204, 336, 405, 420, 390, 324, 231, 120, 285, 480, 595, 640, 625, 560, 455, 320, 165, 385, 660, 836, 924, 935, 880, 770, 616, 429, 220, 506, 880
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OFFSET
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0,2
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COMMENTS
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Kekulé numbers for certain benzenoids. Column 0 yields A000330. Main diagonal yields A000292. Row sums yield A006414.
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LINKS
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FORMULA
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T(n-2,k-1) = n*(2*n-k)*(n-k)*k/6. - M. F. Hasler, Dec 26 2016
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EXAMPLE
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Triangle begins:
1;
5, 4;
14, 16, 10;
30, 40, 35, 20;
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MAPLE
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T:=proc(n, k) if k<=n then (k+1)*(n+2)*(2*n-k+3)*(n-k+1)/6 else 0 fi end: for n from 0 to 10 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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PROG
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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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