A232973 Dziemianczuk's array S(i,j) read by antidiagonals.

1, 3, 6, 15, 33, 60, 81, 189, 378, 675, 459, 1107, 2349, 4509, 7992, 2673, 6588, 14553, 29403, 55188, 97416, 15849, 39663, 90207, 189351, 371358, 687258, 1209951, 95175, 240894, 560115, 1211031, 2458998, 4727565, 8664813, 15227190, 576963, 1473147, 3485187

Offset

0,2

Links

Lars Blomberg, Table of n, a(n) for n = 0..5049 (The first 100 antidiagonals)

M. Dziemianczuk, Counting Lattice Paths With Four Types of Steps, Graphs and Combinatorics, September 2013, DOI 10.1007/s00373-013-1357-1.

Example

Array begins:
     1,     3,     15,      81,      459,      2673,     15849, ...
     6,    33,    189,    1107,     6588,     39663,    240894, ...
    60,   378,   2349,   14553,    90207,    560115,   3485187, ...
   675,  4509,  29403,  189351,  1211031,   7715331,  49045662, ...
  7992, 55188, 371358, 2458998, 16112925, 104838219, 678790125, ...
  ...

Prog

(PARI) \\ Dziemianczuk, Proposition 1
S(n, k)=sum(i=0, n+k, sum(j=0, i, binomial(k, j)*binomial(j, i-j)*binomial(2*k+n-i, k)));
A=[]; for(i=1, 10, A=concat(A, vector(i, j, S(j-1, i-1))));
A \\ Lars Blomberg, Jul 20 2017

Crossrefs

See A122868 and A232969 for leading row row and column.

Sequence in context: A323936 A305839 A322110 * A289006 A336632 A152167

Adjacent sequences: A232970 A232971 A232972 * A232974 A232975 A232976

Keyword

nonn,tabl

Author

N. J. A. Sloane, Dec 05 2013

Extensions

a(15)-a(38) from Lars Blomberg, Jul 20 2017

Status

approved