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A131301
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Regular triangle read by rows: T(n,k) = 3*binomial(floor((n+k)/2),k)-2.
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3
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1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 4, 7, 1, 1, 1, 7, 7, 10, 1, 1, 1, 7, 16, 10, 13, 1, 1, 1, 10, 16, 28, 13, 16, 1, 1, 1, 10, 28, 28, 43, 16, 19, 1, 1, 1, 13, 28, 58, 43, 61, 19, 22, 1, 1, 1, 13, 43, 58, 103, 61, 82, 22, 25, 1, 1, 1, 16, 43, 103, 103, 166, 82
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OFFSET
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0,8
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COMMENTS
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Row sums = A131300: (1, 2, 3, 7, 14, 27, 49, 86, ...). Reversed triangle = A131299.
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LINKS
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FORMULA
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3*A046854 - 2*A000012 as infinite lower triangular matrices (former name).
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EXAMPLE
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First few rows of the triangle:
1;
1, 1;
1, 1, 1;
1, 4, 1, 1;
1, 4, 7, 1, 1;
1, 7, 7, 10, 1, 1;
1, 7, 16, 10, 13, 1, 1;
...
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MAPLE
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for n from 0 to 6 do seq(3*binomial(floor((n+k)/2), k)-2, k=0..n); od; # Nathaniel Johnston, Jun 29 2011
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MATHEMATICA
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t[n_, k_] := 3 Binomial[Floor[(n + k)/2], k] - 2; Table[t[n, k], {n, 11}, {k, 0, n}] // Flatten
(* to view triangle: Table[t[n, k], {n, 5}, {k, 0, n}] // TableForm *) (* Robert G. Wilson v, Feb 28 2015 *)
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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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