A136223
Column 2 of triangle A136220; also equals column 0 of U^3 = A136236 where U = A136228.
Original entry on oeis.org
1, 3, 21, 208, 2637, 40731, 742620, 15624420, 372892266, 9959561867, 294465305959, 9551090908795, 337297690543923, 12886076807637021, 529624555043780909, 23305654066781507361, 1093356525580359412557
Offset: 0
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{a(n)=local(P=Mat(1),U,PShR);if(n==0,1,for(i=0,n+1, PShR=matrix(#P,#P, r,c, if(r>=c,if(r==c,1,if(c==1,0,P[r-1,c-1]))));U=P*PShR^2; U=matrix(#P+1, #P+1, r,c, if(r>=c, if(r<#P+1,U[r,c], if(c==1,(P^3)[ #P,1],(P^(3*c-1))[r-c+1,1])))); P=matrix(#U, #U, r,c, if(r>=c, if(r<#U,P[r,c], (U^c)[r-c+1,1]))));P[n+3,3])}
A136233
Matrix square of triangle U = A136228, read by rows.
Original entry on oeis.org
1, 2, 1, 10, 8, 1, 75, 76, 14, 1, 753, 888, 196, 20, 1, 9534, 12542, 3087, 370, 26, 1, 146353, 209506, 55552, 7320, 598, 32, 1, 2647628, 4058806, 1136975, 159645, 14235, 880, 38, 1, 55251994, 89706276, 26224597, 3856065, 364403, 24480, 1216, 44, 1
Offset: 0
This triangle, U^2, begins:
1;
2, 1;
10, 8, 1;
75, 76, 14, 1;
753, 888, 196, 20, 1;
9534, 12542, 3087, 370, 26, 1;
146353, 209506, 55552, 7320, 598, 32, 1;
2647628, 4058806, 1136975, 159645, 14235, 880, 38, 1;
55251994, 89706276, 26224597, 3856065, 364403, 24480, 1216, 44, 1; ...
where column 0 of U^2 = column 1 of P = A136220.
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{T(n,k)=local(P=Mat(1),U=Mat(1),PShR);if(n>0,for(i=0,n, PShR=matrix(#P,#P, r,c, if(r>=c,if(r==c,1,if(c==1,0,P[r-1,c-1]))));U=P*PShR^2; U=matrix(#P+1, #P+1, r,c, if(r>=c, if(r<#P+1,U[r,c], if(c==1,(P^3)[ #P,1],(P^(3*c-1))[r-c+1,1])))); P=matrix(#U, #U, r,c, if(r>=c, if(r<#R,P[r,c], (U^c)[r-c+1,1])))));(U^2)[n+1,k+1]}
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