cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A034006 Number of n-step self-avoiding walks on the 4-dimensional hypercubic lattice with no non-contiguous adjacencies.

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%I A034006 #36 Aug 03 2020 17:26:23
%S A034006 1,8,56,344,2120,12872,78392,472952,2861768,17223224,103835096,
%T A034006 623927912,3753164744,22526613176,135308002424,811435356200,
%U A034006 4868892591752
%N A034006 Number of n-step self-avoiding walks on the 4-dimensional hypercubic lattice with no non-contiguous adjacencies.
%C A034006 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
%H A034006 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; see Table I, p. 1088 (the case d=4).
%F A034006 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
%Y A034006 Cf. A038746, A038748, A173380, A174319, A323037.
%K A034006 nonn,walk,more
%O A034006 0,2
%A A034006 _N. J. A. Sloane_
%E A034006 Name edited by _Petros Hadjicostas_, Jan 01 2019
%E A034006 Title clarified, a(0), and a(12)-a(16) from _Sean A. Irvine_, Jul 29 2020