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A136238 Matrix cube of triangle W = A136231; also equals P^9, where P = triangle A136220.

%I A136238 #2 Mar 30 2012 18:37:08
%S A136238 1,9,1,99,18,1,1323,306,27,1,21036,5643,621,36,1,390012,115917,14580,
%T A136238 1044,45,1,8287041,2657946,366129,29754,1575,54,1,198918840,67708113,
%U A136238 9968067,882318,52785,2214,63,1,5329794042,1903562412,294952140
%N A136238 Matrix cube of triangle W = A136231; also equals P^9, where P = triangle A136220.
%F A136238 Column k of W^3 (this triangle) = column 2 of W^(k+1), where W = P^3 and P = triangle A136220.
%e A136238 This triangle, W^3, begins:
%e A136238 1;
%e A136238 9, 1;
%e A136238 99, 18, 1;
%e A136238 1323, 306, 27, 1;
%e A136238 21036, 5643, 621, 36, 1;
%e A136238 390012, 115917, 14580, 1044, 45, 1;
%e A136238 8287041, 2657946, 366129, 29754, 1575, 54, 1;
%e A136238 198918840, 67708113, 9968067, 882318, 52785, 2214, 63, 1;
%e A136238 5329794042, 1903562412, 294952140, 27779046, 1804290, 85293, 2961, 72, 1;
%e A136238 where column 0 of W^3 = column 2 of W = triangle A136231.
%o A136238 (PARI) {T(n,k)=local(P=Mat(1),U=Mat(1),W=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]))); W=P^3;));(W^3)[n+1,k+1]}
%Y A136238 Cf. related tables: A136220 (P), A136228 (U), A136230 (V), A136231 (W), A136235 (W^2).
%K A136238 nonn,tabl
%O A136238 0,2
%A A136238 _Paul D. Hanna_, Feb 07 2008