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%I #13 Feb 25 2023 08:23:57
%S 2,4,8,15,26,40,60,84,114,149,190,234,288,346,411,484,565,649,743,840,
%T 947,1063,1185
%N Number of subsequences of {1,2,3,...,n} which are p_1-sequences.
%C A p_k-sequence {x(i)} is one which is strictly monotone increasing,i.e. x(i+1)>x(i) for i=1,2,3,...,n and satisfies the condition that a(k+1)=f(a(k)), for k=1,2,3,...,n-1, where f is a polynomial of degree k with integer coefficients.
%H John W. Layman and Bruce Landman, <a href="https://doi.org/10.1007/BF02192665">Note on the local growth of iterated polynomials</a>, Aeq. Math. 27 (1984), 150-156.
%e {1,2,5,14} is a p_1-subsequence of {1,2,3,...,14}, since 2=f(1), 5=f(2) and 14=f(5) where f is the first degree polynomial given by f(x)=3x-1.
%K nonn,more
%O 1,1
%A _John W. Layman_, Dec 05 2003
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