|
%I #21 Nov 09 2018 07:32:16
%S 2,5,7,3,5,8,2,3,6,5,8,13,6,11,17,4,8,12,10,17,27,12,21,34,9,15,24,20,
%T 34,54,25,42,68,18,30,49,40,68,108,50,85,136,36,61,97,80,135,216,101,
%U 170,271,72,121,194,160,270,430,201,339,541,144,242,387
%N Rectangular array read by rows (n > 0, 1 <= k <= 3): T(n,k) = floor(b(n,k)/2^((A002264(n) + 1)/3)), where b(n,k) = b(n-3,k) + 3*b (n-6,k) + 2*b(n-9,k), with initial values given in comments.
%C From _Franck Maminirina Ramaharo_, Nov 08 2018: (Start)
%C The initial values for b(n,k), 1 <= n <= 9, 1 <= k <= 3, are
%C n\k | 1 2 3
%C ----+---------
%C 1 | 4 8 12
%C 2 | 5 8 13
%C 3 | 4 6 10
%C 4 | 10 16 26
%C 5 | 13 22 35
%C 6 | 9 16 25
%C 7 | 26 44 70
%C 8 | 32 54 86
%C 9 | 23 38 61. (End)
%F From _Franck Maminirina Ramaharo_, Nov 08 2018: (Start)
%F Let M and A denote the following 3 X 3 matrices:
%F 0, 2, 0
%F M = 1, 1, 1
%F 1, 1, 0
%F and
%F 0, 1, 1
%F A = 1, 1, 2
%F 1, 2, 3.
%F Then applying floor() to the entries in (h*M)^(n + 1)*A, where h = 1/(2^(1/3)), yields row 3*n - 2 to 3*n. (End)
%e Array begins:
%e 2, 5, 7;
%e 3, 5, 8;
%e 2, 3, 6;
%e 5, 8, 13;
%e 6, 11, 17;
%e 4, 8, 12;
%e 10, 17, 27;
%e 12, 21, 34;
%e 9, 15, 24;
%e 20, 34, 54;
%e 25, 42, 68;
%e 18, 30, 49;
%e ... - _Franck Maminirina Ramaharo_, Nov 08 2018
%t M = N[4^(1/3)*({{0, 1, 0}, {1, 1, 0}, {0, 0, 0}}/2 + {{0, 1, 0}, {0, 0, 1}, {1, 1, 0}}/2)];
%t A[n_] := M.A[n - 1]; A[0] := {{0, 1, 1}, {1, 1, 2}, {1, 2, 3}};
%t Table[Floor[M.A[n]], {n, 1, 12}]//Flatten
%Y Cf. A097966.
%K nonn,tabf,less
%O 1,1
%A _Roger L. Bagula_, Sep 06 2004
%E Edited, new name, and offset corrected by _Franck Maminirina Ramaharo_, Nov 08 2018
|
