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

Author

Paul D. Hanna, Jan 28 2008

Keywords

• nonn

Crossrefs

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

Programs

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]}

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.