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.

A045649 Number of chiral n-ominoes in n-1 space.

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%I A045649 #13 Jan 12 2019 02:34:15
%S A045649 1,0,0,1,1,1,2,5,9,15,31,70,146,300,656,1471,3258,7245,16400,37461,
%T A045649 85773,197365,457297,1065070,2489750,5842741,13766775,32552087,
%U A045649 77208432,183670145,438176307,1048092760,2513081101
%N A045649 Number of chiral n-ominoes in n-1 space.
%C A045649 Lunnon's DR(n,n-1)-DE(n,n-1). Knuth describes methodology for a similar enumeration, that of free trees with n nodes.
%D A045649 D. E. Knuth, Fundamental Algorithms, 3d Ed. 1997, pp. 386-88.
%H A045649 Vaclav Kotesovec, <a href="/A045649/b045649.txt">Table of n, a(n) for n = 1..1000</a>
%H A045649 W. F. Lunnon, <a href="https://doi.org/10.1093/comjnl/18.4.366">Counting Multidimensional Polyominoes</a>, Computer Journal, Vol. 18 (1975), pp. 366-67.
%F A045649 G.f.: C(x)-C^2(x)/2+C(-x^2)/2 where C(x) is g.f. for same sequence with one cell labeled, A045648.
%F A045649 a(n) ~ c * d^n / n^(5/2), where d = 2.58968405406171542574769690513208346256... and c = 0.36257350770010314582973624284... . - _Vaclav Kotesovec_, Feb 29 2016
%t A045649 s[ n_, k_ ] := s[ n, k ]=c[ n+1-k ]+If[ n<2k, 0, s[ n-k, k ](-1)^k ]; c[ 1 ]=1; c[ n_ ] := c[ n ]=Sum[ c[ i ]s[ n-1, i ]i, {i, 1, n-1} ]/(n-1); Table[ c[ i ]-Sum[ c[ j ]c[ i-j ], {j, 1, i/2} ]+If[ OddQ[ i ], 0, c[ i/2 ](c[ i/2 ]+(-1)^(i/2))/2 ], {i, 1, 33} ]
%Y A045649 Cf. A045648, A000081, A004111.
%K A045649 easy,nice,nonn
%O A045649 1,7
%A A045649 _Robert A. Russell_