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 A177992 Triangle read by rows, A007318 * A177990. 3
 1, 1, 1, 1, 3, 1, 1, 7, 3, 1, 1, 15, 6, 5, 1, 1, 31, 10, 16, 5, 1, 1, 63, 15, 42, 15, 7, 1, 1, 127, 21, 99, 35, 29, 7, 1, 1, 255, 28, 219, 70, 93, 28, 9, 1, 1, 511, 36, 466, 126, 256, 84, 46, 9, 1, 1, 1023, 45, 968, 210, 638, 210, 176, 45, 11, 1, 1, 2047, 55, 1981, 330, 1486, 462, 562, 165, 67, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums = A045623: (1, 2, 5, 12, 28, 64, 144, ...). Double Riordan array ( 1/(1 - x); x/(1 - 2*x), x*(1 - 2*x)/(1 - x)^2 ) as defined in Davenport et al. - Peter Bala, Aug 25 2021 LINKS Table of n, a(n) for n=0..77. D. E. Davenport, L. W. Shapiro and L. C. Woodson, The Double Riordan Group, The Electronic Journal of Combinatorics, 18(2) (2012). FORMULA As infinite lower triangular matrices, A007318 * A177990. From Peter Bala, Aug 25 2021: (Start) T(n,2*k) = T(n-1,2*k-1) - T(n-1,2*k+1). T(n,2*k+1) = 2*T(n-1,2*k+1) + T(n-1,2*k). G.f.: A(x,t) = (1 - t)/(1 - 2*t)*(1 - 2*t + t*x)/((1 - t)^2 - t^2*x^2) = 1 + (1 + x)*t + (1 + 3*x + x^2)^t^2 + .... G.f. column 2*k: x^(2*k)/(1 - x)^(2*k+1). G.f. column 2*k+1: x^(2*k+1)/((1 - x)^(2*k+1) * (1 - 2*x)). (End) EXAMPLE First few rows of the triangle: 1; 1, 1; 1, 3, 1; 1, 7, 3, 1; 1, 15, 6, 5, 1; 1, 31, 10, 16, 5, 1; 1, 63, 15, 42, 15, 7, 1; 1, 127, 21, 99, 35, 29, 7, 1; 1, 255, 28, 219, 70, 93, 28, 9, 1; 1, 511, 36, 466, 126, 256, 84, 46, 9, 1; 1, 1023, 45, 968, 210, 638, 210, 176, 45, 11, 1; 1, 2047, 55, 1981, 330, 1486, 462, 562, 165, 67, 11, 1; 1, 4095, 66, 4017, 495, 3302, 924, 1586, 495, 299, 66, 13, 1; ... CROSSREFS Cf. A177993 = A177990 * A007318. Cf. A045623, A070909. Sequence in context: A332538 A071812 A248133 * A346906 A228524 A116407 Adjacent sequences: A177989 A177990 A177991 * A177993 A177994 A177995 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, May 16 2010 EXTENSIONS a(8) corrected and more terms by Georg Fischer, Dec 28 2021 STATUS approved

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Last modified March 1 08:00 EST 2024. Contains 370430 sequences. (Running on oeis4.)