cp's OEIS Frontend

A097964 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.

%I A097964 #21 Nov 09 2018 07:32:16
%S A097964 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 A097964 34,54,25,42,68,18,30,49,40,68,108,50,85,136,36,61,97,80,135,216,101,
%U A097964 170,271,72,121,194,160,270,430,201,339,541,144,242,387
%N A097964 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 A097964 From _Franck Maminirina Ramaharo_, Nov 08 2018: (Start)
%C A097964 The initial values for b(n,k), 1 <= n <= 9, 1 <= k <= 3, are
%C A097964 n\k |  1  2  3
%C A097964 ----+---------
%C A097964   1 |  4  8 12
%C A097964   2 |  5  8 13
%C A097964   3 |  4  6 10
%C A097964   4 | 10 16 26
%C A097964   5 | 13 22 35
%C A097964   6 |  9 16 25
%C A097964   7 | 26 44 70
%C A097964   8 | 32 54 86
%C A097964   9 | 23 38 61. (End)
%F A097964 From _Franck Maminirina Ramaharo_, Nov 08 2018: (Start)
%F A097964 Let M and A denote the following 3 X 3 matrices:
%F A097964       0, 2, 0
%F A097964   M = 1, 1, 1
%F A097964       1, 1, 0
%F A097964 and
%F A097964       0, 1, 1
%F A097964   A = 1, 1, 2
%F A097964       1, 2, 3.
%F A097964 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 A097964 Array begins:
%e A097964    2,  5,  7;
%e A097964    3,  5,  8;
%e A097964    2,  3,  6;
%e A097964    5,  8, 13;
%e A097964    6, 11, 17;
%e A097964    4,  8, 12;
%e A097964   10, 17, 27;
%e A097964   12, 21, 34;
%e A097964    9, 15, 24;
%e A097964   20, 34, 54;
%e A097964   25, 42, 68;
%e A097964   18, 30, 49;
%e A097964    ... - _Franck Maminirina Ramaharo_, Nov 08 2018
%t A097964 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 A097964 A[n_] := M.A[n - 1]; A[0] := {{0, 1, 1}, {1, 1, 2}, {1, 2, 3}};
%t A097964 Table[Floor[M.A[n]], {n, 1, 12}]//Flatten
%Y A097964 Cf. A097966.
%K A097964 nonn,tabf,less
%O A097964 1,1
%A A097964 _Roger L. Bagula_, Sep 06 2004
%E A097964 Edited, new name, and offset corrected by _Franck Maminirina Ramaharo_, Nov 08 2018