1,2

Equals the first differences of A129092: a(n) = A129092(n+1) - A129092(n). Equals the row sums of the matrix square of triangle A129100.

This sequence also equals the row sums of the triangle formed from

the semi-Fibonacci numbers (A030067) with 2^n terms in row n for n>=0:

n=0: 1;

n=1: 1, 2;

n=2: 1, 3, 2, 5;

n=3: 1, 6, 3, 9, 2, 11, 5, 16;

n=4: 1, 17, 6, 23, 3, 26, 9, 35, 2, 37, 11, 48, 5, 53, 16, 69; ...

and the right-most border equals A129092(n) = A030067(2^n - 1).

The semi-Fibonacci numbers (A030067) start:

[1, (1), 2, 1, (3), 2, 5, 1, 6, 3, 9, 2, (11), 5, 16, 1, ...],

and obey the recurrence:

A030067(n) = A030067(n/2) when n is even; and

A030067(n) = A030067(n-1) + A030067(n-2) when n is odd.

This sequence also equals row sums of matrix square A129100^2:

1;

2, 1;

6, 4, 1;

24, 20, 8, 1;

136, 136, 72, 16, 1;

1162, 1360, 880, 272, 32, 1; ...

(PARI) /* As row sums of the matrix square of triangle A129100: */ {a(n)=local(A=Mat(1), B); for(m=1, n+1, 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(sum(k=1, n, (A^2)[n, k]))}

Cf. A030067; A129092, A129094.

Sequence in context: A121580 A081367 A156171 this_sequence A057325 A054700 A009280

Adjacent sequences: A129090 A129091 A129092 this_sequence A129094 A129095 A129096

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Mar 29 2007