A071950 Triangle read by rows of numbers of paths in a lattice satisfying certain conditions.

1, 1, 1, 2, 2, 5, 1, 5, 12, 3, 14, 31, 1, 9, 38, 83, 4, 28, 106, 227, 1, 14, 84, 301, 634, 5, 48, 252, 864, 1799, 1, 20, 157, 758, 2508, 5171, 6, 75, 504, 2283, 7348, 15027, 1, 27, 265, 1602, 6897, 21699, 44074, 7, 110, 906, 5056, 20903, 64526, 130299, 1, 35, 417, 3035, 15894, 63552, 193055, 387880

Offset

0,4

Comments

The Riordan array ( (1-x-sqrt(1-2*x-3*x^2-4*x^3))/(2*x^2*(1+x)), (1-x-sqrt(1-2*x-3*x^2-4*x^3))/(2*x*(1+x)) ) read downwards antidiagonals. - R. J. Mathar, Oct 31 2011

Links

Table of n, a(n) for n=0..63.

D. Merlini, D. G. Rogers, R. Sprugnoli and M. C. Verri, On some alternative characterizations of Riordan arrays, Canad J. Math., 49 (1997), 301-320.

Example

Triangle begins:
  1;
  1;
  1,  2;
  2,  5;
  1,  5,  12;
  3, 14,  31;
  1,  9,  38,   83;
  4, 28, 106,  227;
  1, 14,  84,  301,  634;
  5, 48, 252,  864, 1799;
  1, 20, 157,  758, 2508,  5171;
  6, 75, 504, 2283, 7348, 15027;
  1, 27, 265, 1602, 6897, 21699, 44074;

Maple

read("transforms3") ;
A071950 := proc(d, c)
        local g, h, n, k ;
        n := (d + (d mod 2))/2+c ;
        k := (d-(d mod 2))/2-c ;
        g := (1-x-sqrt(1-2*x-3*x^2-4*x^3))/2/x^2/(1+x) ;
        h := (1-x-sqrt(1-2*x-3*x^2-4*x^3))/2/x/(1+x) ;
        RIORDAN(g, h, n, k) ;
end proc:
for n from 0 to 12 do
        for k from 0 to floor(n/2) do
                printf("%d, ", A071950(n, k)) ;
        end do:
        printf("\n") ;
end do; # R. J. Mathar, Oct 31 2011

Crossrefs

Sequence in context: A079300 A128932 A286150 * A274847 A165922 A337293

Adjacent sequences: A071947 A071948 A071949 * A071951 A071952 A071953

Keyword

nonn,easy,tabf,changed

Author

N. J. A. Sloane, Jun 15 2002

Status

approved