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%I #32 Jan 31 2021 20:02:35
%S 0,0,24,192,1032,5376,26688,128880,605664,2802576,12755136,57525552,
%T 256574352,1137418464,5001796944,21899428128,95296531680,413331190896
%N Number of configurations of linear chains in a cubic lattice.
%C From _Petros Hadjicostas_, Jan 04 2019: (Start)
%C In the notation of Nemirovsky et al. (1992), a(n), the n-th term of the current sequence is C_{n,m} with m=1 (and d=3). Here, for a d-dimensional hypercubic lattice, C_{n,m} is "the number of configurations of an n-bond self-avoiding chain with m neighbor contacts." (For d=2, we have C_{n,m=1} = A033155(n).)
%C 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).
%C 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. 1090-1093. See also the comments for sequence A038748 by Bert Dobbelaere. (End)
%H A. M. Nemirovsky, K. F. Freed, T. Ishinabe, and J. F. Douglas, <a href="http://dx.doi.org/10.1007/BF01049010">Marriage of exact enumeration and 1/d expansion methods: lattice model of dilute polymers</a>, J. Statist. Phys., 67 (1992), 1083-1108.
%F a(n) = 24*A038747(n) + 48*A038749(n) for n >= 1. - _Petros Hadjicostas_, Jan 04 2019
%Y Cf. A033155, A038747, A038748, A038749.
%K nonn,more
%O 1,3
%A _N. J. A. Sloane_
%E Name edited by _Petros Hadjicostas_, Jan 04 2019
%E a(12)-a(18) from _Sean A. Irvine_, Jan 31 2021
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