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 A096591 Triangle T, read by rows, such that the matrix square shifts T one place diagonally left and upward, with T(n,0)=T(n,n)=1 for n>=0. 2
 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 5, 5, 2, 1, 1, 1, 8, 10, 5, 2, 1, 1, 1, 15, 22, 14, 5, 2, 1, 1, 1, 28, 47, 34, 14, 5, 2, 1, 1, 1, 61, 113, 88, 42, 14, 5, 2, 1, 1, 1, 133, 269, 223, 116, 42, 14, 5, 2, 1, 1, 1, 328, 705, 609, 333, 132, 42, 14, 5, 2, 1, 1, 1, 807, 1843, 1660 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Column with index 1 forms the row sums shift right. The convergent of the rows in reverse order is the Catalan sequence (A000108). LINKS Table of n, a(n) for n=0..81. FORMULA T(n, k) = Sum_{i=0..n-1} T(n-2, i)*T(i, k-1) for n>1 and k>0; T(n, 0)=T(n, n)=1. EXAMPLE Rows begin: [1], [1,1], [1,1,1], [1,2,1,1], [1,3,2,1,1], [1,5,5,2,1,1], [1,8,10,5,2,1,1], [1,15,22,14,5,2,1,1], [1,28,47,34,14,5,2,1,1], [1,61,113,88,42,14,5,2,1,1], [1,133,269,223,116,42,14,5,2,1,1],... The matrix square of T is given by: [1], [2,1], [3,2,1], [5,5,2,1], [8,10,5,2,1], [15,22,14,5,2,1], [28,47,34,14,5,2,1], [61,113,88,42,14,5,2,1], [133,269,223,116,42,14,5,2,1],... which equals T shift one place diagonally left and upward. PROG (PARI) T(n, k)=if(n

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Last modified September 10 19:02 EDT 2024. Contains 375794 sequences. (Running on oeis4.)