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1, 2, 1, 3, 3, 1, 2, 6, 5, 1, 1, 5, 12, 6, 1, 2, 3, 14, 17, 8, 1, 3, 7, 14, 24, 26, 9, 1, 2, 12, 27, 30, 45, 33, 11, 1, 1, 9, 45, 62, 70, 66, 45, 12, 1, 2, 5, 44, 111, 147, 120, 104, 54, 14, 1, 3, 11, 39, 128, 273, 273, 217, 140, 69, 15, 1, 2, 18, 65, 139, 366, 546, 518, 329, 200, 80, 17, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Row sums = 1, 3, 7, 14, 25, 45, 85, ... (This is probably a new sequence and should be added to the OEIS.) - N. J. A. Sloane, Aug 09 2019
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LINKS
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FORMULA
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EXAMPLE
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First few rows of the triangle are:
1,
2, 1,
3, 3, 1,
2, 6, 5, 1,
1, 5, 12, 6, 1,
2, 3, 14, 17, 8, 1,
3, 7, 14, 24, 26, 9, 1,
...
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PROG
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(PARI) T007318(n, k) = binomial(n, k);
T065941(n, k) = binomial(n - (k+1)\2, k\2);
T049310(n, k) = if ((n+k)%2, 0, (-1)^((n+k)/2 + k) * binomial((n+k)/2, k));
T(n, k) = T007318(n, k) + T065941(n, k) - T049310(n, k); \\ Michel Marcus, Apr 28 2014
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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The old definition of A131376 did not match the data, as Michel Marcus pointed out. The definition there has been corrected, keeping the old data. The present sequence uses the old definition with corrected data from Michel Marcus. - N. J. A. Sloane, Aug 09 2019
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STATUS
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approved
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