[seqfan] Re: Error?

N. J. A. Sloane njas at research.att.com
Sat Nov 14 21:00:55 CET 2009

Richard Guy said:

In more detail, I have difficulty reconciling

    A033507  with  A005178


%I A033507
%S A033507 5,71,823,10012,120465,1453535,17525619,211351945,2548684656,
%T A033507 30734932553,370635224561,4469527322891,53898461609719,
%U A033507 649966808093412,7838012982224913,94519361817920403
%N A033507 Number of matchings in graph P_{4} X P_{n}

%I A005178 M3813
%S A005178 0,1,1,5,11,36,95,281,781,2245,6336,18061,51205,145601,413351,1174500,
%T A005178 3335651,9475901,26915305,76455961,217172736,616891945,1752296281,
%U A005178 4977472781,14138673395,40161441636,114079985111,324048393905
%N A005178 Number of perfect matchings (or domino tilings) in 4 X (n-1) rectangle.

Could the difference be that the first counts all matchings,
while the second counts perfect matchings?

However, I agree that the definition of A005178
is confusing.  The tiling definition refers to tiling
a "chess-board" of size 4 X somthing, while
the matching definition refers to the graph
formed with nodes at the centers of the squuares
of the board.

I'll do some editing

 Best regards

More information about the SeqFan mailing list