A096569 - OEIS

%I #5 Mar 30 2012 18:57:05

%S 1,0,1,2,2,5,9,14,25,46,78,136,242,419,733,1291,2251,3938,6905,12073,

%T 21129,37001,64741,113304,198344,347126,607532,1063387,1861149,

%U 3257410,5701362,9978711,17465052,30568232,53501720,93640745,163894183

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

%F 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.)

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

%K nonn

%O 1,4

%A _Clark Kimberling_, Jun 27 2004