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A034006 Configurations of linear chains in a 4-dimensional hypercubic lattice. 7
8, 56, 344, 2120, 12872, 78392, 472952, 2861768, 17223224, 103835096, 623927912 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In the notation of Nemirovsky et al. (1992), a(n), the n-th term of the current sequence is C_{n,m} with m=0 (and d=4). 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,0) = A173380(n), while for d=3, we have C(n,0) = A174319(n).) - Petros Hadjicostas, Jan 02 2019

LINKS

Table of n, a(n) for n=1..11.

A. M. Nemirovsky, K. F. Freed, T. Ishinabe, and J. F. Douglas, Marriage of exact enumeration and 1/d expansion methods: lattice model of dilute polymers, J. Statist. Phys., 67 (1992), 1083-1108; see Table I, p. 1088 (the case d=4).

FORMULA

a(n) = 8 + 48*A038746(n) + 192*A038748(n) + 384*A323037(n). (It can be proved using Eq. (5) in Nemirovsky et al. (1992).) - Petros Hadjicostas, Jan 02 2019

CROSSREFS

Cf. A038746, A038748, A173380, A174319, A323037.

Sequence in context: A319891 A319872 A215227 * A307813 A291387 A272773

Adjacent sequences:  A034003 A034004 A034005 * A034007 A034008 A034009

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

Name edited by Petros Hadjicostas, Jan 01 2019

STATUS

approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)