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Triangle read by rows of numbers of paths in a lattice satisfying certain conditions.
1

%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