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

Author

N. J. A. Sloane, Dec 05 2013

Keywords

• nonn
• tabl

Examples

			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, ...
  ...
		

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.

Crossrefs

See A122868 and A232969 for leading row row and column.

Programs

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

Extensions

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