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 A191582 Riordan matrix (1/(1-3*x^2),x/(1-x)). 2
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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. LINKS FORMULA 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). EXAMPLE 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 MATHEMATICA Flatten[Table[Sum[Binomial[n-2i-1, n-k-2i]3^i, {i, 0, ((n-k))/2}], {n, 0, 20}, {k, 0, n}]] PROG (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); CROSSREFS Cf. A167936, A191584, A191585. Sequence in context: A006941 A076277 A130115 * A130160 A162169 A216954 Adjacent sequences:  A191579 A191580 A191581 * A191583 A191584 A191585 KEYWORD nonn,easy,tabl AUTHOR Emanuele Munarini, Jun 07 2011 STATUS approved

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