
COMMENTS

From Petros Hadjicostas, Jan 04 2019: (Start)
In the notation of Nemirovsky et al. (1992), a(n), the nth term of the current sequence is C_{n,m} with m=1 (and d=3). Here, for a ddimensional hypercubic lattice, C_{n,m} is "the number of configurations of an nbond selfavoiding chain with m neighbor contacts." (For d=2, we have C_{n,m=1} = A033155(n).)
These numbers are given in Table I (p. 1088) in the paper by Nemirovsky et al. (1992). Using Eqs. (5) and (7b) in the paper, we can prove that C_{n,m=1} = 2^1*1!*Bin(3,1)*p_{n,m=1}^{(1)} + 2^2*2!*Bin(3,2)*p_{n,m=1}^{(2)} + 2^3*3!*Bin(3,3)*p_{n,m=1}^{(3)} = 0 + 24*p_{n,m=1}^{(2)} + 48*p_{n,m=1}^{(3)} = 24*A038747(n) + 48*A038749(n).
For an explanation of the meaning of p_{n,m}^{(l)} (l = 1,2,3,...), see the discussion that follows Eq. (5) in Nemirovsky et al. (1992), pp. 10901093. See also the comments for sequence A038748 by Bert Dobbelaere. (End)
