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.

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

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