A136232 - OEIS

%I #4 Mar 14 2015 11:56:23

%S 1,4,1,24,8,1,198,76,12,1,2116,888,156,16,1,28052,12542,2350,264,20,1,

%T 446560,209506,41034,4864,400,24,1,8325700,4058806,821562,100988,8710,

%U 564,28,1,178284892,89706276,18631332,2352116,209440,14168,756,32,1

%N Triangle, read by rows, equal to the matrix 4th power of triangle A136220.

%F Column k of this triangle = column 1 of U^(k+1) where U = A136228.

%e This triangle P^4 begins:

%e 1,

%e 4, 1;

%e 24, 8, 1;

%e 198, 76, 12, 1;

%e 2116, 888, 156, 16, 1;

%e 28052, 12542, 2350, 264, 20, 1;

%e 446560, 209506, 41034, 4864, 400, 24, 1;

%e 8325700, 4058806, 821562, 100988, 8710, 564, 28, 1;

%e 178284892, 89706276, 18631332, 2352116, 209440, 14168, 756, 32, 1; ...

%e where column k = column 1 of U^(k+1);

%e triangle U = A136228 begins:

%e 1;

%e 1, 1;

%e 3, 4, 1;

%e 15, 24, 7, 1;

%e 108, 198, 63, 10, 1;

%e 1036, 2116, 714, 120, 13, 1;

%e 12569, 28052, 9884, 1725, 195, 16, 1; ...

%e where column k of U = column 0 of P^(3k+1) and

%e triangle P = A136220 begins:

%e 1;

%e 1, 1;

%e 3, 2, 1;

%e 15, 10, 3, 1;

%e 108, 75, 21, 4, 1;

%e 1036, 753, 208, 36, 5, 1;

%e 12569, 9534, 2637, 442, 55, 6, 1; ...

%o (PARI) {T(n,k)=local(P=Mat(1),U,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])))));(P^4)[n+1,k+1]}

%Y Cf. A136229 (column 0); related tables: A136220 (P), A136228 (U).

%K nonn,tabl

%O 0,2

%A _Paul D. Hanna_, Jan 28 2008