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%I A185624 #5 Mar 30 2012 18:37:25
%S A185624 1,2,1,3,2,1,6,7,2,1,18,28,11,2,1,79,142,66,15,2,1,463,913,470,120,19,
%T A185624 2,1,3396,7244,3997,1098,190,23,2,1,30073,69004,40079,11587,2122,276,
%U A185624 27,2,1,314037,771359,466448,140092,26707,3638,378,31,2,1,3796561,9933242,6208551,1921122
%N A185624  Triangle, read by rows, equal to the matrix square of triangle A185620.
%e A185624  Triangle begins:
%e A185624 1;
%e A185624 2, 1;
%e A185624 3, 2, 1;
%e A185624 6, 7, 2, 1;
%e A185624 18, 28, 11, 2, 1;
%e A185624 79, 142, 66, 15, 2, 1;
%e A185624 463, 913, 470, 120, 19, 2, 1;
%e A185624 3396, 7244, 3997, 1098, 190, 23, 2, 1;
%e A185624 30073, 69004, 40079, 11587, 2122, 276, 27, 2, 1;
%e A185624 314037, 771359, 466448, 140092, 26707, 3638, 378, 31, 2, 1;
%e A185624 3796561, 9933242, 6208551, 1921122, 377495, 53149, 5742, 496, 35, 2, 1; ...
%e A185624 This triangle equals the matrix square, R^2, of triangle R = A185620, which begins:
%e A185624 1;
%e A185624 1, 1;
%e A185624 1, 1, 1;
%e A185624 1, 3, 1, 1;
%e A185624 1, 10, 5, 1, 1;
%e A185624 1, 42, 27, 7, 1, 1;
%e A185624 1, 226, 173, 52, 9, 1, 1;
%e A185624 1, 1525, 1330, 442, 85, 11, 1, 1;
%e A185624 1, 12555, 12134, 4345, 897, 126, 13, 1, 1; ...
%e A185624 where R^3 - R^2 + I equals R shifted left one column.
%o A185624  (PARI) {T(n, k)=local(A=Mat(1), B); for(m=1, n, B=A^3-A^2+A^0; A=matrix(m+1, m+1); for(i=1, m+1, for(j=1, i, if(i<2|j==i, A[i, j]=1, if(j==1, A[i, j]=1, A[i, j]=B[i-1, j-1]))))); return((A^2)[n+1, k+1])}
%Y A185624  Cf. A185620, A185625, A185626, A185627, A185628.
%K A185624 nonn,tabl
%O A185624 0,2
%A A185624 _Paul D. Hanna_, Sep 07 2011

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