login
This site is supported by donations to The OEIS Foundation.

 

Logo

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A258708 Triangle read by rows: T(i,j) = integer part of binomial(i+j,i-j)/(2*j+1), 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 the 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, A. F. Horadam, Divisibility Criteria and Sequence Generators Associated with Fermat Coefficients, Preprint, 1980.

EXAMPLE

Triangle begins:

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: A050446 A214868 A144048 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 28 21:38 EDT 2017. Contains 287241 sequences.