%I A094954
%S A094954 1,1,1,1,2,1,1,3,5,1,1,4,11,13,1,1,5,19,41,34,1,1,6,29,91,153,89,1,1,7,
%T A094954 41,169,436,571,233,1,1,8,55,281,985,2089,2131,610,1,1,9,71,433,1926,
%U A094954 5741,10009,7953,1597,1,1,10,89,631,3409,13201,33461,47956,29681
%N A094954 Array T(k,n) read by antidiagonals. G.f.: x(1-x)/(1-kx+x^2), k>1.
%C A094954 Also, values of polynomials with coefficients in A098493 (see Fink et 
               al.). See A098495 for negative k.
%C A094954 Number of dimer tilings of the graph S_{k-1} X P_{2n-2}.
%D A094954 A. Fink, R. K. Guy and M. Krusemeyer, Partitions with parts occurring 
               at most thrice, in preparation.
%H A094954 Elizabeth Wilmer, <a href="http://www.oberlin.edu/math/faculty/wilmer/
               OEISconj87.pdf">A note on Stephan's conjecture 87</a>
%F A094954 Recurrence: T(k, 1) = 1, T(k, 2) = k-1, T(k, n) = kT(k, n-1) - T(k, n-2).
%F A094954 For n>3, T(k, n) = [k(k-2) + T(k, n-1)T(k, n-2)] / T(k, n-3).
%F A094954 T(k, n+1) = S(n, k) - S(n-1, k) = U(n, k/2) - U(n-1, k/2), with S, U 
               = Chebyshev polynomials of second kind.
%F A094954 T(k+2, n+1) = Sum[i=0..n, k^(n-i) * C(2n-i, i)] (from comments by Benoit 
               Cloitre).
%e A094954 1,1,1,1,1,1,1,1,1,1,1,1,1,1, ...
%e A094954 1,2,5,13,34,89,233,610,1597, ...
%e A094954 1,3,11,41,153,571,2131,7953, ...
%e A094954 1,4,19,91,436,2089,10009,47956, ...
%e A094954 1,5,29,169,985,5741,33461,195025, ...
%e A094954 1,6,41,281,1926,13201,90481,620166, ...
%o A094954 (PARI) T(k,n)=polcoeff(x*(1-x)/(1-k*x+x*x),n)
%Y A094954 Rows are first differences of rows in array A073134.
%Y A094954 Rows 2-14 are A000012, A001519, A079935/A001835, A004253, A001653, A049685, 
               A070997, A070998, A072256, A078922, A077417, A085260, A001570. Other 
               rows: A007805 (k=18), A075839 (k=20), A077420 (k=34), A078988 (k=66).
%Y A094954 Columns include A028387. Diagonals include A094955, A094956. Antidiagonal 
               sums are A094957.
%Y A094954 Sequence in context: A121207 A097084 A143327 this_sequence A083064 A112338 
               A111672
%Y A094954 Adjacent sequences: A094951 A094952 A094953 this_sequence A094955 A094956 
               A094957
%K A094954 nonn,tabl
%O A094954 1,5
%A A094954 Ralf Stephan (ralf(AT)ark.in-berlin.de), May 31 2004