The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A179607 Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + 2*x - 4*x^2)/(1 - 2*x - 8*x^2). 2
 1, 4, 12, 56, 208, 864, 3392, 13696, 54528, 218624, 873472, 3495936, 13979648, 55926784, 223690752, 894795776, 3579117568, 14316601344, 57266143232, 229065097216, 916259340288, 3665039458304, 14660153638912, 58640622944256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The a(n) represent the number of n-move routes of a fairy chess piece starting in the central square (m = 5) on a 3 X 3 chessboard. This fairy chess piece behaves like a king on the eight side and corner squares but on the central square the king goes crazy and turns into a red king, see A179596. The sequence above corresponds to just one red king vector, i.e., A[5] vector, with decimal [binary] value 325 [1,0,1,0,0,0,1,0,1]. This vectors leads for the corner squares to A083424 and for the side squares to A003947. The inverse binomial transform of A100284 (without the first leading 1). LINKS Table of n, a(n) for n=0..23. Index entries for linear recurrences with constant coefficients, signature (2, 8). FORMULA G.f.: (1 + 2*x - 4*x^2)/(1 - 2*x - 8*x^2). a(n) = 2*a(n-1) + 8*a(n-2), for n >= 3, with a(0) = 1, a(1) = 4 and a(2) = 12. a(n) = 5*(4)^(n)/6 - (-2)^(n)/3 for n >= 1 and a(0) = 1. a(n) = 4*A083424(n-1), n>0. - R. J. Mathar, Mar 08 2021 MAPLE with(LinearAlgebra): nmax:=24; m:=5; A[1]:= [0, 1, 0, 1, 1, 0, 0, 0, 0]: A[2]:= [1, 0, 1, 1, 1, 1, 0, 0, 0]: A[3]:= [0, 1, 0, 0, 1, 1, 0, 0, 0]: A[4]:= [1, 1, 0, 0, 1, 0, 1, 1, 0]: A[5]:= [1, 0, 1, 0, 0, 0, 1, 0, 1]: A[6]:= [0, 1, 1, 0, 1, 0, 0, 1, 1]: A[7]:= [0, 0, 0, 1, 1, 0, 0, 1, 0]: A[8]:= [0, 0, 0, 1, 1, 1, 1, 0, 1]: A[9]:= [0, 0, 0, 0, 1, 1, 0, 1, 0]: A:=Matrix([A[1], A[2], A[3], A[4], A[5], A[6], A[7], A[8], A[9]]): 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 Join[{1}, LinearRecurrence[{2, 8}, {4, 12}, 30]] (* Harvey P. Dale, Mar 01 2012 *) CROSSREFS Cf. A179597 (central square). Sequence in context: A298680 A149421 A051195 * A149422 A149423 A295496 Adjacent sequences: A179604 A179605 A179606 * A179608 A179609 A179610 KEYWORD easy,nonn AUTHOR Johannes W. Meijer, Jul 28 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 25 06:14 EDT 2024. Contains 371964 sequences. (Running on oeis4.)