A129101 Column 1 of triangle A129100; also equals column 0 of the matrix square of A129100.

1, 2, 6, 24, 136, 1162, 15702, 346768, 12836904, 814033666, 90074891654, 17659668432744, 6211830230882472, 3960850942657072026, 4617438765658479411542, 9912250203901899238148640

Offset: 0

Author

Paul D. Hanna, Mar 29 2007

Keywords

• nonn

Crossrefs

Cf. A129100 (triangle); A129092 (column 0), A129102 (column 2), A129103 (column 3).

Programs

PARI

a(n)=local(A=Mat(1),B);for(m=1,n+2,B=matrix(m,m);for(r=1,m,for(c=1,r, if(r==c || r==1 || r==2,B[r,c]=1,if(c==1,B[r,1]=sum(i=1,r-1,A[r-1,i]), B[r,c]=(A^(2^(c-1)))[r-c+1,1])); )); A=B); return(A[n+2,2])

Formula

a(n) = A129094(n+1) - A129093(n); a(n) = A030067(2^(n+1)+2^n-1) - A030067(2^(n+1)-3) for n>=0 where A030067 is the semi-Fibonacci numbers.