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A071950
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Triangle read by rows of numbers of paths in a lattice satisfying certain conditions.
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1
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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
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OFFSET
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0,4
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COMMENTS
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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
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LINKS
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EXAMPLE
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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;
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MAPLE
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read("transforms3") ;
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
end do:
printf("\n") ;
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CROSSREFS
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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STATUS
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approved
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