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A218073 Number of profiles in domino tiling of a 2*n checkboard.

%I A218073 #27 Jan 05 2025 19:51:39
%S A218073 0,1,2,9,12,50,60,245,280,1134,1260,5082,5544,22308,24024,96525,
%T A218073 102960,413270,437580,1755182,1847560,7407036,7759752,31097794,
%U A218073 32449872,130007500,135207800,541574100,561632400,2249204040,2326762800,9316746045,9617286240,38504502630
%N A218073 Number of profiles in domino tiling of a 2*n checkboard.
%H A218073 Alois P. Heinz, <a href="/A218073/b218073.txt">Table of n, a(n) for n = 0..1000</a>
%H A218073 T. C. Wu, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/21-4/wu.pdf">Counting the Profiles in Domino Tiling</a>, The Fibonacci Quarterly, Volume 21, Number 4, November 1983, pp. 302-304.
%F A218073 If n is even, a(n) = binomial(n, n/2)*n/2.
%F A218073 If n is odd, a(n) = binomial(n + 1, (n + 1)/2)*n/2.
%p A218073 a:= proc(n) option remember;
%p A218073       `if`(n<3, n, (n*(5-7*n)*a(n-1) +4*(n-2)*(7*n+16)*a(n-3)
%p A218073       +(24-12*n+172*n^2)*a(n-2))/ ((n+1)*(43*n-89)))
%p A218073     end:
%p A218073 seq(a(n), n=0..40);  # _Alois P. Heinz_, Oct 20 2012
%t A218073 a[n_] := n/2*Binomial[n + Mod[n, 2], (n + Mod[n, 2])/2]; Table[a[n], {n, 0, 33}] (* _Jean-François Alcover_, Feb 22 2013, after _Joerg Arndt_ *)
%o A218073 (Maxima) a[0]:0$a[1]:1$a[2]:2$
%o A218073 a[n]:=(n*(5-7*n)*a[n-1] +4*(n-2)*(7*n+16)*a[n-3]+(24-12*n+172*n^2)*a[n-2])/ ((n+1)*(43*n-89))$
%o A218073 makelist(a[n] ,n,0,40); /* _Martin Ettl_, Oct 21 2012 */
%o A218073 (PARI) a(n) = n/2 * binomial(n+(n%2),(n+n%2)/2); /* _Joerg Arndt_, Oct 21 2012 */
%Y A218073 Cf. A005430 (bisection).
%K A218073 nonn
%O A218073 0,3
%A A218073 _Michel Marcus_, Oct 20 2012