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

0,2

Comments

Matrix square equals triangle A135893.

Links

Table of n, a(n) for n=0..46.

Example

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.

Prog

(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]}

Crossrefs

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

Sequence in context: A127894 A127898 A078938 * A329433 A258245 A133366

Adjacent sequences: A135885 A135886 A135887 * A135889 A135890 A135891

Keyword

nonn,tabl

Author

Paul D. Hanna, Dec 15 2007

Status

approved