A136227 Column 1 of triangle A136225; also equals column 0 of triangle A136230.

1, 4, 26, 232, 2657, 37405, 627435, 12248365, 273211787, 6862775083, 191840407156, 5909873159107, 199002812894375, 7273866200397039, 286882936292798852, 12145886485652450131, 549504341899436759416

Offset

0,2

Comments

Equals column 1 of P^2 (A136225) and equals column 0 of V^2, where P = A136220 and V = A136230 are triangular matrices such that column k of V = column 0 of P^(3k+2) and column j of P^2 = column 0 of V^(j+1).

Links

Table of n, a(n) for n=0..16.

Prog

(PARI) /* Generate using matrix product recurrences of triangle P=A136220: */ {a(n)=local(P=Mat([1, 0; 1, 1]), U, PShR); if(n>0, for(i=0, n+1, 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+2, 2]}

Crossrefs

Cf. A136226, A136225 (P^2), A136220 (P), A136230 (V); A136217.

Sequence in context: A107879 A066224 A227917 * A346978 A000310 A054360

Adjacent sequences: A136224 A136225 A136226 * A136228 A136229 A136230

Keyword

nonn

Author

Paul D. Hanna, Jan 28 2008

Status

approved