Search: id:A094954 Results 1-1 of 1 results found. %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 note on Stephan's conjecture 87 %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 Search completed in 0.005 seconds