# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a290764 Showing 1-1 of 1 %I A290764 #15 Dec 30 2023 13:17:36 %S A290764 3,15,54,174,537,1629,4908,14748,44271,132843,398562,1195722,3587205, %T A290764 10761657,32285016,96855096,290565339,871696071,2615088270,7845264870, %U A290764 23535794673,70607384085,211822152324,635466457044,1906399371207,5719198113699,17157594341178 %N A290764 Number of (non-null) connected induced subgraphs in the 2 X n king graph. %C A290764 a(n) is also the number of 4-cycles in the (n+1)-Dorogovtsev-Goltsev-Mendes graph (using the indexing convention that the 0-Dorogovtsev-Goltsev-Mendes graph is P_2). - _Eric W. Weisstein_, Dec 06 2023 %H A290764 Eric Weisstein's World of Mathematics, Connected Graph. %H A290764 Eric Weisstein's World of Mathematics, Dorogovtsev-Goltsev-Mendes Graph. %H A290764 Eric Weisstein's World of Mathematics, Graph Cycle. %H A290764 Eric Weisstein's World of Mathematics, King Graph. %H A290764 Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph. %H A290764 Index entries for linear recurrences with constant coefficients, signature (5, -7, 3). %F A290764 a(n) = 3/4*(3^(n + 1) - 2*n - 3). %F A290764 a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3). %F A290764 G.f.: -((3 x)/((-1 + x)^2 (-1 + 3 x))). %t A290764 Table[3/4 (3^(n + 1) - 2 n - 3), {n, 20}] %t A290764 LinearRecurrence[{5, -7, 3}, {3, 15, 54}, 40] %t A290764 CoefficientList[Series[-3/((-1 + x)^2 (-1 + 3 x)), {x, 0, 20}], x] %Y A290764 Cf. A003462(n) (3-cycles), A367967(n) (5-cycles), A367968(n) (6-cycles). %K A290764 nonn,easy %O A290764 1,1 %A A290764 _Eric W. Weisstein_, Aug 10 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE