A096569 Number of compositions of n with first part 1 and no equal adjacent parts; this is column 1 of the array in A096568.

1, 0, 1, 2, 2, 5, 9, 14, 25, 46, 78, 136, 242, 419, 733, 1291, 2251, 3938, 6905, 12073, 21129, 37001, 64741, 113304, 198344, 347126, 607532, 1063387, 1861149, 3257410, 5701362, 9978711, 17465052, 30568232, 53501720, 93640745, 163894183

Offset: 1

Author

Clark Kimberling, Jun 27 2004

Keywords

• nonn

Crossrefs

Cf. A003242, A096568, A096570, A096571, A096572.

Formula

Define s(0)=1, T(1, 1)=1 and T(i, j)=0 for j>i. For n>=2 and 1<=k<=n, define s(n)=T(n, 1)+T(n, 2)+...+T(n, n) and T(n, k)=s(n-k)-T(n-k, k). (This is array A096568.)