This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A180030 Number of n-move paths on a 3 X 3 chessboard of a queen starting or ending in a corner or side square. 3
 1, 6, 38, 238, 1494, 9374, 58822, 369102, 2316086, 14533246, 91194918, 572240558, 3590762134, 22531735134, 141384772742, 887177744782, 5566966905846, 34932256487486, 219197017684198, 1375443140320878, 8630791843077974 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The a(n) represent the number of n-move paths of a chess queen starting or ending in a given corner or side square (m = 1, 3, 7, 9; 2, 4, 6, 8) on a 3 X 3 chessboard. The central square leads to A180031. To determine the a(n) we can either sum the components of the column vector A^n[k,m], with A the adjacency matrix of the queen's graph, or we can sum the components of the row vector A^n[m,k], see the Maple program. Closely related with this sequence are the red queen sequences, see A180028 and A180032. Inverse binomial transform of A015555 (without the leading 0). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (5, 8). FORMULA G.f.: (1+x)/(1 - 5*x - 8*x^2). a(n) = 5*a(n-1) + 8*a(n-2) with a(0) = 1 and a(1) = 6. a(n) = ((7+11*A)*A^(-n-1) + (7+11*B)*B^(-n-1))/57 with A = (-5+sqrt(57))/16 and B = (-5-sqrt(57))/16. MAPLE with(LinearAlgebra): nmax:=20; m:=1; A[5]:= [1, 1, 1, 1, 0, 1, 1, 1, 1]: A:=Matrix([[0, 1, 1, 1, 1, 0, 1, 0, 1], [1, 0, 1, 1, 1, 1, 0, 1, 0], [1, 1, 0, 0, 1, 1, 1, 0, 1], [1, 1, 0, 0, 1, 1, 1, 1, 0], A[5], [0, 1, 1, 1, 1, 0, 0, 1, 1], [1, 0, 1, 1, 1, 0, 0, 1, 1], [0, 1, 0, 1, 1, 1, 1, 0, 1], [1, 0, 1, 0, 1, 1, 1, 1, 0]]): for n from 0 to nmax do B(n):=A^n: a(n):= add(B(n)[m, k], k=1..9): od: seq(a(n), n=0..nmax); MATHEMATICA LinearRecurrence[{5, 8}, {1, 6}, 201] (* Vincenzo Librandi, Nov 15 2011 *) PROG (MAGMA) I:=[1, 6]; [n le 2 select I[n] else 5*Self(n-1)+8*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 15 2011 CROSSREFS Sequence in context: A026296 A037499 A037676 * A135030 A217633 A162558 Adjacent sequences:  A180027 A180028 A180029 * A180031 A180032 A180033 KEYWORD nonn,easy AUTHOR Johannes W. Meijer, Aug 09 2010 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 March 19 13:29 EDT 2019. Contains 321330 sequences. (Running on oeis4.)