A135888 Triangle, read by rows, equal to the matrix cube of triangle P = A135880.

1, 3, 1, 12, 6, 1, 63, 39, 9, 1, 421, 300, 81, 12, 1, 3472, 2741, 816, 138, 15, 1, 34380, 29380, 9366, 1716, 210, 18, 1, 399463, 363922, 122148, 23647, 3105, 297, 21, 1, 5344770, 5135894, 1795481, 362116, 49880, 5088, 399, 24, 1, 81097517, 81557270

Offset: 0

Author

Paul D. Hanna, Dec 15 2007

Keywords

• nonn
• tabl

Comments

Matrix square equals triangle A135893.

Examples

			Triangle P^3 begins:
1;
3, 1;
12, 6, 1;
63, 39, 9, 1;
421, 300, 81, 12, 1;
3472, 2741, 816, 138, 15, 1;
34380, 29380, 9366, 1716, 210, 18, 1;
399463, 363922, 122148, 23647, 3105, 297, 21, 1;
5344770, 5135894, 1795481, 362116, 49880, 5088, 399, 24, 1;
81097517, 81557270, 29478724, 6138746, 875935, 93306, 7770, 516, 27, 1;
where P = A135880 begins:
1;
1, 1;
2, 2, 1;
6, 7, 3, 1;
25, 34, 15, 4, 1;
138, 215, 99, 26, 5, 1;
970, 1698, 814, 216, 40, 6, 1; ...
where column k of P^2 equals column 0 of P^(2k+2)
such that column 0 of P^2 equals column 0 of P shift left.
		

Crossrefs

Cf. columns: A135889, A135890; related tables: A135880 (P), A135894 (R), A135893 (P^6).

Programs

PARI

{T(n,k)=local(P=Mat(1),R,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]))));R=P*PShR; R=matrix(#P+1, #P+1, r,c, if(r>=c, if(r<#P+1,R[r,c], if(c==1,(P^2)[ #P,1],(P^(2*c-1))[r-c+1,1])))); P=matrix(#R, #R, r,c, if(r>=c, if(r<#R,P[r,c], (R^c)[r-c+1,1])))));(P^3)[n+1,k+1]}