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A109244
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A tree-node counting triangle.
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2
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1, 1, 1, 4, 2, 1, 13, 7, 3, 1, 46, 24, 11, 4, 1, 166, 86, 40, 16, 5, 1, 610, 314, 148, 62, 22, 6, 1, 2269, 1163, 553, 239, 91, 29, 7, 1, 8518, 4352, 2083, 920, 367, 128, 37, 8, 1, 32206, 16414, 7896, 3544, 1461, 541, 174, 46, 9, 1, 122464, 62292, 30086, 13672, 5776, 2232
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OFFSET
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0,4
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COMMENTS
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Columns include A026641,A014300,A014301. Inverse matrix is A109246. Row sums are A014300. Diagonal sums are A109245.
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LINKS
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Table of n, a(n) for n=0..60.
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FORMULA
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Number triangle T(n, k)=sum{i=0..n, (-1)^(n-i)binomial(n+i-k, i-k)}; Riordan array (1/(1-xc(x)-2x^2*c(x)^2), xc(x)) where c(x)=g.f. of A000108.
The production matrix M (discarding the zeros) is:
1, 1;
3, 1, 1;
3, 1, 1, 1;
3, 1, 1, 1, 1;
... such that the n-th row of the triangle is the top row of M^n. - Gary W. Adamson, Feb 16 2012
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EXAMPLE
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Rows begin
1;
1,1;
4,2,1;
13,7,3,1;
46,24,11,4,1;
166,86,40,16,5,1;
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CROSSREFS
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Sequence in context: A183158 A174005 A152818 * A171650 A225476 A143777
Adjacent sequences: A109241 A109242 A109243 * A109245 A109246 A109247
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry, Jun 23 2005
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STATUS
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approved
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