The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A338100 Number of spanning trees in the n X 2 king graph. 2
 1, 16, 192, 2304, 27648, 331776, 3981312, 47775744, 573308928, 6879707136, 82556485632, 990677827584, 11888133931008, 142657607172096, 1711891286065152, 20542695432781824, 246512345193381888, 2958148142320582656, 35497777707846991872, 425973332494163902464, 5111679989929966829568 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Eric Weisstein's World of Mathematics, King Graph Eric Weisstein's World of Mathematics, Spanning Tree Index entries for linear recurrences with constant coefficients, signature (12). FORMULA a(n) = 12 * a(n-1) for n > 2. a(n) = 3^(n-2) * 4^n for n > 1. G.f.: x*(1 + 4*x)/(1 - 12*x). - Stefano Spezia, Nov 29 2020 PROG (Python) # Using graphillion from graphillion import GraphSet def make_nXk_king_graph(n, k):     grids = []     for i in range(1, k + 1):         for j in range(1, n):             grids.append((i + (j - 1) * k, i + j * k))             if i < k:                 grids.append((i + (j - 1) * k, i + j * k + 1))             if i > 1:                 grids.append((i + (j - 1) * k, i + j * k - 1))     for i in range(1, k * n, k):         for j in range(1, k):             grids.append((i + j - 1, i + j))     return grids def A338029(n, k):     if n == 1 or k == 1: return 1     universe = make_nXk_king_graph(n, k)     GraphSet.set_universe(universe)     spanning_trees = GraphSet.trees(is_spanning=True)     return spanning_trees.len() def A338100(n):     return A338029(n, 2) print([A338100(n) for n in range(1, 20)]) CROSSREFS Column 2 of A338029. Sequence in context: A317601 A000767 A053539 * A218176 A120994 A016178 Adjacent sequences:  A338097 A338098 A338099 * A338101 A338102 A338103 KEYWORD nonn,easy AUTHOR Seiichi Manyama, Nov 29 2020 STATUS approved

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

Last modified June 23 04:15 EDT 2021. Contains 345395 sequences. (Running on oeis4.)