cp's OEIS Frontend

A097966 Rectangular array read by rows (n > 0, 1 <= k <= 3): T(n,k) = floor(b(n,k)/6^(2*(A002264(n) + 1)/3)), where b(n,k) = b(n-3,k) + 13*b (n-6,k) + 36*b(n-9,k), with initial values given in comments.

%I A097966 #14 Nov 09 2018 07:31:00
%S A097966 1,2,3,1,2,4,2,3,4,1,3,4,2,4,6,2,5,6,3,5,7,3,7,9,4,7,10,4,8,11,6,10,
%T A097966 14,6,11,15,7,12,17,9,16,22,10,17,23,11,19,26,14,24,33,15,26,36,17,29,
%U A097966 40,21,37,51,23,40,55,26,45,62,33,57,77,35,61,83
%N A097966 Rectangular array read by rows (n > 0, 1 <= k <= 3): T(n,k) = floor(b(n,k)/6^(2*(A002264(n) + 1)/3)), where b(n,k) = b(n-3,k) + 13*b (n-6,k) + 36*b(n-9,k), with initial values given in comments.
%C A097966 From _Franck Maminirina Ramaharo_, Nov 08 2018: (Start)
%C A097966 The initial values for b(n,k), 1 <= n <= 9, 1 <= k <= 3, are
%C A097966 n\k |    1    2    3
%C A097966 ----+---------------
%C A097966   1 |   16   32   36
%C A097966   2 |   17   30   44
%C A097966   3 |   24   36   51
%C A097966   4 |   68  120  176
%C A097966   5 |  105  170  233
%C A097966   6 |   99  186  240
%C A097966   7 |  420  680  932
%C A097966   8 |  470  848 1129
%C A097966   9 |  519  870 1227. (End)
%F A097966 From _Franck Maminirina Ramaharo_, Nov 08 2018: (Start)
%F A097966 Let M and A denote the following 3 X 3 matrices:
%F A097966       0, 4, 0
%F A097966   M = 1, 1, 3
%F A097966       3, 3, 0
%F A097966 and
%F A097966       0, 1, 1
%F A097966   A = 1, 1, 2
%F A097966       1, 2, 2.
%F A097966 Then applying floor() to the entries in (h*M)^(n + 1)*A, where h = 1/(6^(2/3)), yields row 3*n - 2 to 3*n. (End)
%e A097966 Triangle begins:
%e A097966   1,  2,  3;
%e A097966   1,  2,  4;
%e A097966   2,  3,  4;
%e A097966   1,  3,  4;
%e A097966   2,  4,  6;
%e A097966   2,  5,  6;
%e A097966   3,  5,  7;
%e A097966   3,  7,  9;
%e A097966   4,  7, 10;
%e A097966   4,  8, 11;
%e A097966   6, 10, 14;
%e A097966   6, 11, 15;
%e A097966    ... - _Franck Maminirina Ramaharo_, Nov 08 2018
%t A097966 M = N[(16/9)^(1/3)*({{0, 1, 0}, {1, 1, 0}, {0, 0, 0}}*(1/4) + {{0, 1, 0}, {0, 0, 1}, {1, 1, 0}}*(3/4))];
%t A097966 A[n_] := M.A[n - 1]; A[0] := {{0, 1, 1}, {1, 1, 2}, {1, 2, 2}};
%t A097966 Table[Floor[M.A[n]], {n, 1, 12}]//Flatten
%Y A097966 Cf. A097964.
%K A097966 nonn,tabf,less
%O A097966 1,2
%A A097966 _Roger L. Bagula_, Sep 06 2004
%E A097966 Edited, new name, and offset corrected by _Franck Maminirina Ramaharo_, Nov 08 2018