A136226 Column 0 of P^2 where triangle P = A136220; also equals column 1 of square array A136217.

1, 2, 8, 49, 414, 4529, 61369, 996815, 18931547, 412345688, 10143253814, 278322514093, 8432315243347, 279689506725247, 10083429764179733, 392703359698462567, 16433405366965493214, 735484032071079495354

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

Equals column 0 of triangle V = A136230, where column k of V = column 0 of P^(3k+2) such that column k of P^2 = column 0 of V^(k+1), for k>=0 and where P = A136220.

Prog

(PARI) /* Generate using matrix product recurrences of triangle P=A136220: */ {a(n)=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^2)[n+1, 1]}

Crossrefs

Cf. A136225 (P^2), A136220 (P), A136230 (V); A136217.

Sequence in context: A088181 A058864 A332237 * A046165 A227264 A114619

Adjacent sequences: A136223 A136224 A136225 * A136227 A136228 A136229

Keyword

nonn

Author

Paul D. Hanna, Jan 28 2008

Status

approved