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 A258708 Triangle read by rows: T(i,j) = integer part of binomial(i+j, i-j)/(2*j+1) for i >= 1 and j = 0..i-1. 16
 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 7, 4, 1, 1, 7, 14, 12, 5, 1, 1, 9, 25, 30, 18, 6, 1, 1, 12, 42, 66, 55, 26, 7, 1, 1, 15, 66, 132, 143, 91, 35, 8, 1, 1, 18, 99, 245, 334, 273, 140, 45, 9, 1, 1, 22, 143, 429, 715, 728, 476, 204, 57, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS In the Loh-Shannon-Horadam paper, Table 3 contains a typo (see Extensions lines). T(n,k) = round(A258993(n,k)/(2*k+1)). - Reinhard Zumkeller, Jun 22 2015 From Reinhard Zumkeller, Jun 23 2015: (Start) (using tables 4 and 5 of the Loh-Shannon-Horadam paper, p. 8f). T(n, n-1)  = 1; T(n, n-2)  = n for n > 1; T(n, n-3)  = A000969(n-3) for n > 2; T(n, n-4)  = A000330(n-3) for n > 3; T(n, n-5)  = T(2*n-7, 2) = A000970(n) for n > 4; T(n, n-6)  = A000971(n) for n > 5; T(n, n-7)  = A000972(n) for n > 6; T(n, n-8)  = A000973(n) for n > 7; T(n, 1)    = A001840(n-1) for n > 1; T(2*n, n)  = A001764(n); T(3*n-1, 1) = A000326(n); T(3*n, 2*n) = A002294(n); T(4*n, 3*n) = A002296(n). (End) LINKS Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened R. P. Loh, A. G. Shannon, and A. F. Horadam, Divisibility Criteria and Sequence Generators Associated with Fermat Coefficients, Preprint, 1980. EXAMPLE Triangle T(i, j) (with rows i >= 1 and columns j >= 0) begins as follows:   1;   1,  1;   1,  2,  1;   1,  3,  3,   1;   1,  5,  7,   4,   1;   1,  7, 14,  12,   5,   1;   1,  9, 25,  30,  18,   6,   1;   1, 12, 42,  66,  55,  26,   7,  1;   1, 15, 66, 132, 143,  91,  35,  8, 1;   1, 18, 99, 245, 334, 273, 140, 45, 9, 1;   ... PROG (Haskell) a258708 n k = a258708_tabl !! (n-1) !! k a258708_row n = a258708_tabl !! (n-1) a258708_tabl = zipWith (zipWith ((round .) . ((/) `on` fromIntegral)))                        a258993_tabl a158405_tabl -- Reinhard Zumkeller, Jun 22 2015, Jun 16 2015 CROSSREFS Cf. A011793. Cf. A007318, A258993, A158405, A005408, A006013 (central terms). Cf. A000326, A000330, A000969, A000970, A000971, A000972, A000973, A000976, A001764, A001840, A002294, A002296. Sequence in context: A214868 A144048 A292193 * A113983 A199333 A089980 Adjacent sequences:  A258705 A258706 A258707 * A258709 A258710 A258711 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Jun 12 2015 EXTENSIONS Corrected T(8,5) = 26 from Reinhard Zumkeller, Jun 13 2015 STATUS approved

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Last modified August 13 04:54 EDT 2020. Contains 336442 sequences. (Running on oeis4.)