[seqfan] Re: Error?

[N. J. A. Sloane]

Richard Guy said:

In more detail, I have difficulty reconciling

    A033507  with  A005178
...

Me:

%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
 			 Neil