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 A071950 Triangle read by rows of numbers of paths in a lattice satisfying certain conditions. 1
 1, 1, 1, 2, 2, 5, 1, 5, 12, 3, 14, 31, 1, 9, 38, 83, 4, 28, 106, 227, 1, 14, 84, 301, 634, 5, 48, 252, 864, 1799, 1, 20, 157, 758, 2508, 5171, 6, 75, 504, 2283, 7348, 15027, 1, 27, 265, 1602, 6897, 21699, 44074, 7, 110, 906, 5056, 20903, 64526, 130299, 1, 35, 417, 3035, 15894, 63552, 193055, 387880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The Riordan array ( (1-x-sqrt(1-2x-3x^2-4x^3))/(2x^2(1+x)), (1-x-sqrt(1-2x-3x^2-4x^3))/(2x(1+x)) read downwards antidiagonals. - R. J. Mathar, Oct 31 2011 LINKS Table of n, a(n) for n=0..63. D. Merlini, D. G. Rogers, R. Sprugnoli and M. C. Verri, On some alternative characterizations of Riordan arrays, Canad J. Math., 49 (1997), 301-320. EXAMPLE 1; 1; 1,2; 2,5; 1,5,12; 3,14,31; 1,9,38,83; 4,28,106,227; 1,14,84,301,634; 5,48,252,864,1799; 1,20,157,758,2508,5171; 6,75,504,2283,7348,15027; 1,27,265,1602,6897,21699,44074; MAPLE read("transforms3") ; A071950 := proc(d, c) local g, h, n, k ; n := (d + (d mod 2))/2+c ; k := (d-(d mod 2))/2-c ; g := (1-x-sqrt(1-2*x-3*x^2-4*x^3))/2/x^2/(1+x) ; h := (1-x-sqrt(1-2*x-3*x^2-4*x^3))/2/x/(1+x) ; RIORDAN(g, h, n, k) ; end proc: for n from 0 to 12 do for k from 0 to floor(n/2) do printf("%d, ", A071950(n, k)) ; end do: printf("\n") ; end do; # R. J. Mathar, Oct 31 2011 CROSSREFS Sequence in context: A079300 A128932 A286150 * A274847 A165922 A337293 Adjacent sequences: A071947 A071948 A071949 * A071951 A071952 A071953 KEYWORD nonn,easy,tabf AUTHOR N. J. A. Sloane, Jun 15 2002 STATUS approved

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Last modified November 30 03:37 EST 2023. Contains 367452 sequences. (Running on oeis4.)