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A191582
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Riordan matrix (1/(1-3*x^2),x/(1-x)).
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2
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1, 0, 1, 3, 1, 1, 0, 4, 2, 1, 9, 4, 6, 3, 1, 0, 13, 10, 9, 4, 1, 27, 13, 23, 19, 13, 5, 1, 0, 40, 36, 42, 32, 18, 6, 1, 81, 40, 76, 78, 74, 50, 24, 7, 1, 0, 121, 116, 154, 152, 124, 74, 31, 8, 1, 243, 121, 237, 270, 306, 276, 198, 105, 39, 9, 1, 0, 364, 358, 507, 576, 582, 474, 303, 144, 48, 10, 1, 729, 364, 722, 865, 1083, 1158, 1056, 777, 447, 192, 58, 11, 1
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OFFSET
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0,4
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COMMENTS
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Row sums = A167936(n+1).
Diagonal sums = A191584.
Central coefficients = A191585.
Alternated row sums: sum((-1)^(n-k)T(n,k),k=0..n) = 3^(floor(n/2)) (A167936).
Binomial row sums: sum(binomial(n,k)*T(n,k),k=0..n) = central coefficients.
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LINKS
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Table of n, a(n) for n=0..90.
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FORMULA
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T(n,k) = sum(binomial(n-2*i-1,n-k-2*i)*3^i,i=0..(n-k)/2).
Recurrence: T(n+1,k+1) = T(n,k) + T(n,k+1).
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EXAMPLE
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Triangle begins:
1
0, 1
3, 1, 1
0, 4, 2, 1
9, 4, 6, 3, 1
0, 13, 10, 9, 4, 1
27, 13, 23, 19, 13, 5, 1
0, 40, 36, 42, 32, 18, 6, 1
81, 40, 76, 78, 74, 50, 24, 7, 1
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MATHEMATICA
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Flatten[Table[Sum[Binomial[n-2i-1, n-k-2i]3^i, {i, 0, ((n-k))/2}], {n, 0, 20}, {k, 0, n}]]
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PROG
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(Maxima) create_list(sum(binomial(n-2*i-1, n-k-2*i)*3^i, i, 0, (n-k)/2), n, 0, 20, k, 0, n);
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CROSSREFS
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Cf. A167936, A191584, A191585.
Sequence in context: A006941 A076277 A130115 * A130160 A162169 A216954
Adjacent sequences: A191579 A191580 A191581 * A191583 A191584 A191585
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Emanuele Munarini, Jun 07 2011
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STATUS
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approved
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