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 A140045 Sequence generated from Z/6Z addition table considered as a matrix. 1
 1, 40, 495, 8616, 124011, 1905804, 28383615, 427423824, 6403870611, 96118424820, 1441505073735, 21624751859256, 324361491427611, 4865500724823324, 72982158337539855, 1094735196058294944, 16421015247083935011, 246315330264968309700, 3694729496968781349975 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A140044 = the analogous sequence for Z/5Z; A095897 for Z/4Z and A007070 for Z/3Z. LINKS Table of n, a(n) for n=1..19. Index entries for linear recurrences with constant coefficients, signature (12,93,-576,-2592,5184,19440). FORMULA Let X = the Z/6Z addition table considered as a matrix: [0,1,2,3,4,5; 1,2,3,4,5,0; 2,3,4,5,0,1; 3,4,5,0,1,2; 4,5,0,1,2,3; 5,0,1,2,3,4]. a(n) = term (1,2) of X^n. G.f.: -x*(216*x^4-468*x^3-78*x^2+28*x+1) / ((3*x+1)*(6*x-1)*(6*x+1)*(15*x-1)*(12*x^2-1)). - Colin Barker, May 25 2013 EXAMPLE a(3) = 495 since term (1,2) of X^3 = 495. MAPLE a:= n-> (Matrix(6, (i, j)-> irem(i+j-2, 6))^n)[1, 2]: seq(a(n), n=0..20); # Alois P. Heinz, May 25 2013 CROSSREFS Cf. A140044, A095897, A007070. Sequence in context: A271650 A177096 A202902 * A223162 A069079 A093744 Adjacent sequences: A140042 A140043 A140044 * A140046 A140047 A140048 KEYWORD nonn,easy AUTHOR Gary W. Adamson and Roger L. Bagula, May 02 2008 EXTENSIONS More terms from Colin Barker, May 25 2013 STATUS approved

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Last modified April 21 04:54 EDT 2024. Contains 371850 sequences. (Running on oeis4.)