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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A179601 Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1+4*x)/(1 - 2*x - 10*x^2 - 4*x^3). 2
 1, 6, 22, 108, 460, 2088, 9208, 41136, 182704, 813600, 3618784, 16104384, 71651008, 318820992, 1418569600, 6311953152, 28084886272, 124963582464, 556023840256, 2474023050240, 11008138832896, 48980603529216, 217938687588352 (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 6 red king vectors, i.e., A[5] vectors, with decimal values 335, 359, 365, 455, 461 and 485. These vectors lead for the corner squares to A179600 and for the side squares to A123347. LINKS Index entries for linear recurrences with constant coefficients, signature (2,10,4). FORMULA G.f.: ( -1-4*x ) / ( (2*x+1)*(2*x^2 + 4*x - 1) ). a(n) = 2*a(n-1) + 10*a(n-2) + 4*a(n-3) with a(0)=1, a(1)=6 and a(2)=22. a(n) = (-2/5)*(-1/2)^(-n) + ((2+3*A)*A^(-n-1) + (2+3*B)*B^(-n-1))/10 with A = (-1+sqrt(6)/2) and B = (-1-sqrt(6)/2). Lim_{k->infinity} a(n+k)/a(k) = (-1)^(n+1)*A016116(n+1)/(A041007(n-1)*sqrt(6) - A041006(n-1)) for n => 1. MAPLE with(LinearAlgebra): nmax:=22; 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, 1, 1, 0, 0, 0, 1, 1, 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); CROSSREFS Cf. A179597 (central square). Sequence in context: A078418 A100300 A027296 * A151495 A193463 A319214 Adjacent sequences: A179598 A179599 A179600 * A179602 A179603 A179604 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 March 25 23:47 EDT 2023. Contains 361529 sequences. (Running on oeis4.)