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%I #16 Apr 13 2019 13:54:49
%S 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,
%T 48,252,864,1799,1,20,157,758,2508,5171,6,75,504,2283,7348,15027,1,27,
%U 265,1602,6897,21699,44074,7,110,906,5056,20903,64526,130299,1,35,417,3035,15894,63552,193055,387880
%N Triangle read by rows of numbers of paths in a lattice satisfying certain conditions.
%C The Riordan array ( (1-x-sqrt(1-2x-3x^2-4x^3))/(2x^2(1+x)), (1-x-sqrt(1-2x-3x^2-4x^3))/(2x(1+x)) read downwards antidiagonals. - _R. J. Mathar_, Oct 31 2011
%H D. Merlini, D. G. Rogers, R. Sprugnoli and M. C. Verri, <a href="http://dx.doi.org/10.4153/CJM-1997-015-x">On some alternative characterizations of Riordan arrays</a>, Canad J. Math., 49 (1997), 301-320.
%e 1;
%e 1;
%e 1,2;
%e 2,5;
%e 1,5,12;
%e 3,14,31;
%e 1,9,38,83;
%e 4,28,106,227;
%e 1,14,84,301,634;
%e 5,48,252,864,1799;
%e 1,20,157,758,2508,5171;
%e 6,75,504,2283,7348,15027;
%e 1,27,265,1602,6897,21699,44074;
%p read("transforms3") ;
%p A071950 := proc(d,c)
%p local g,h,n,k ;
%p n := (d + (d mod 2))/2+c ;
%p k := (d-(d mod 2))/2-c ;
%p g := (1-x-sqrt(1-2*x-3*x^2-4*x^3))/2/x^2/(1+x) ;
%p h := (1-x-sqrt(1-2*x-3*x^2-4*x^3))/2/x/(1+x) ;
%p RIORDAN(g,h,n,k) ;
%p end proc:
%p for n from 0 to 12 do
%p for k from 0 to floor(n/2) do
%p printf("%d,", A071950(n,k)) ;
%p end do:
%p printf("\n") ;
%p end do; # _R. J. Mathar_, Oct 31 2011
%K nonn,easy,tabf
%O 0,4
%A _N. J. A. Sloane_, Jun 15 2002
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