A063395 T(2n,n) with T(n,m) as in A063394.

1, 3, 19, 131, 979, 7683, 62099, 511619, 4271699, 36018179, 305998099, 2615234691, 22459983059, 193665818115, 1675580699539, 14538892408451, 126467748738899, 1102484411211779, 9629327766561299, 84247346901823619, 738200425192338899, 6477139329614712323

Offset: 0

Author

Floor van Lamoen, Jul 16 2001

Keywords

• nonn

Crossrefs

Equals 4*A084771(n-1) - 1, n>0.

Programs

PARI

m=matrix(50,50):for(i=1,50,m[1,i]=1:m[i,1]=1):for(i=2,50, for(k=1,i,x=i-k+1: if(m[x,k]==0,m[x,k]=sum(n=2,k-1,m[x,n])+sum(n=2,x-1,m[n,k])+k+x-1))):for(n=1,24,print1(m[n,n]",")) /* Ralf Stephan */

Formula

G.f.: 4x/sqrt(1-10x+9x^2) + (1-2x)/(1-x). - Ralf Stephan, Mar 23 2004

Conjecture: (-n+1)*a(n) +(11*n-17)*a(n-1) +(-19*n+43)*a(n-2) +9*(n-3)*a(n-3)=0. - R. J. Mathar, Jun 10 2013

Extensions

More terms from Ralf Stephan, Mar 23 2004