The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A289900 Number of maximal matchings in the n-triangular honeycomb rook graph. 2
 1, 1, 3, 9, 135, 2025, 212625, 22325625, 21097715625, 19937341265625, 207248662456171875, 2154349846231906640625, 291128066470548703880859375, 39341591262497599098939931640625, 79746389028864195813528714933837890625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Also the number of maximum matchings for n > 1. The n-triangular honeycomb rook graph is the disjoint union of the complete graphs K_k for k in {1..n}. In terms of a triangular chessboard it is the graph for a chesspiece that is constrained to move on a single axis. - Andrew Howroyd, Jul 17 2017 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..50 Eric Weisstein's World of Mathematics, Matching Eric Weisstein's World of Mathematics, Maximal Independent Edge Set FORMULA a(n) = Product_{k=1..n} A001147(ceiling(k/2)). - Andrew Howroyd, Jul 17 2017 MATHEMATICA MapAt[# - 1 &, #, 1] &@ FoldList[Times, Array[(2 Ceiling[#/2] - 1)!! &, 15]] (* Michael De Vlieger, Jul 18 2017 *) FoldList[Times, Table[(k - Mod[k - 1, 2])!!, {k, 15}]] (* Eric W. Weisstein, Jul 19 2017 *) Table[Product[(k - Mod[k - 1, 2])!!, {k, n}], {n, 15}] (* Eric W. Weisstein, Jul 19 2017 *) Table[2^(n (n + 2)/4 - 1/12)  E^(-1/4) Pi^(-(n + 1)/2) Glaisher^3 If[Mod[n, 2] == 0, BarnesG[(3 + n)/2]^2, 2^(1/4) BarnesG[n/2 + 1] BarnesG[n/2 + 2]], {n, 15}] (* Eric W. Weisstein, Jul 19 2017 *) PROG (PARI) a(n)=prod(k=1, n, k!/((k\2)!*2^(k\2))); \\ Andrew Howroyd, Jul 17 2017 (Python) from sympy import factorial2, ceiling from operator import mul def a001147(n):     return factorial2(2*n - 1) def a(n):     return reduce(mul, [a001147(ceiling(k/2)) for k in range(1, n + 1)]) print([a(n) for n in range(1, 31)]) # Indranil Ghosh, Jul 18 2017, after PARI code CROSSREFS Cf. A289897. Sequence in context: A141143 A163402 A288757 * A235062 A082707 A087193 Adjacent sequences:  A289897 A289898 A289899 * A289901 A289902 A289903 KEYWORD nonn AUTHOR Eric W. Weisstein, Jul 14 2017 EXTENSIONS Terms a(11) and beyond from Andrew Howroyd, Jul 17 2017 a(1) changed to 1 by N. J. A. Sloane, Jul 18 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 29 07:07 EDT 2022. Contains 357082 sequences. (Running on oeis4.)