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 A159974 Triangle read by rows, M * Q; M = an infinite lower triangular Toeplitz matrix with (1, 1, 2, 3, 4, 5, ...) in every column. Q = a matrix with A034943: (1, 1, 2, 5, 12, 28, ...) as the main diagonal and the rest zeros. 1
 1, 1, 1, 2, 1, 2, 3, 2, 2, 5, 4, 3, 4, 5, 12, 5, 4, 6, 10, 12, 28, 6, 5, 8, 15, 24, 28, 65, 7, 6, 10, 20, 36, 56, 65, 151, 8, 7, 12, 25, 48, 84, 130, 151, 351, 9, 8, 14, 30, 60, 112, 195, 302, 351, 816, 10, 9, 16, 35, 72, 140, 260, 453, 702, 816, 1897 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,4 COMMENTS Row sums = A034943 starting (1, 2, 5, 12, 28, 65, 151, 351, ...). As a property of eigentriangles, sum of n-th row terms = rightmost term of next row. A034943 starting (1, 2, 5, 12, 28, ...) = the INVERT transform of (1, 1, 2, 3, 4, 5, ...). LINKS Table of n, a(n) for n=2..67. FORMULA Triangle read by rows, M * Q; M = an infinite lower triangular Toeplitz matrix with (1, 1, 2, 3, 4, 5, ...) in every column. Q = a matrix with A034943: (1, 1, 2, 5, 12, 28, ...) as the main diagonal and the rest zeros. EXAMPLE First few rows of the triangle: 1; 1, 1; 2, 1, 2; 3, 2, 2, 5; 4, 3, 4, 5, 12; 5, 4, 6, 10, 12, 28; 6, 5, 8, 15, 24, 28, 65; 7, 6, 10, 20, 36, 56, 65, 151; 8, 7, 12, 25, 48, 84, 130, 151, 351; 9, 8, 14, 30, 60, 112, 195, 302, 351, 816; 10, 9, 16, 35, 72, 140, 260, 453, 702, 816, 1897; ... Example: row 6 = (4, 3, 4, 5, 12) = termwise products of (1, 1, 2, 5, 12) and (4, 3, 2, 1, 1). CROSSREFS Cf. A034943. Sequence in context: A172366 A132148 A237829 * A143866 A155002 A182413 Adjacent sequences: A159971 A159972 A159973 * A159975 A159976 A159977 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Apr 28 2009 STATUS approved

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Last modified June 20 05:29 EDT 2024. Contains 373512 sequences. (Running on oeis4.)