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A132742 Triangle T(n,m) = 1 + ((2*n*3^m) mod 12), read by rows.

%I A132742 #44 Sep 08 2022 08:45:31
%S A132742 1,3,7,5,1,1,7,7,7,7,9,1,1,1,1,11,7,7,7,7,7,1,1,1,1,1,1,1,3,7,7,7,7,7,
%T A132742 7,7,5,1,1,1,1,1,1,1,1,7,7,7,7,7,7,7,7,7,7,9,1,1,1,1,1,1,1,1,1,1,11,7,
%U A132742 7,7,7,7,7,7,7,7,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A132742 Triangle T(n,m) = 1 + ((2*n*3^m) mod 12), read by rows.
%C A132742 T(n,m) differs from A132728 in the order in which n and m are handled.
%H A132742 Stefano Spezia, <a href="/A132742/b132742.txt">First 150 rows of the triangle, flattened</a>
%F A132742 T(n,m) = 1 + ((2*n*3^m) mod 12).
%F A132742 T(n,m) = 1 + ((A005843(n)*A000244(m)) mod 12). - _Stefano Spezia_, Dec 26 2018
%F A132742 Bivariate g.f.: -(4*x^7*y^2 + 8*x^6*y^2 - x^6*y - 7*x^5*y + 4*x^4*y^2 - 11*x^5 - x^4*y - 4*x^3*y^2 - 9*x^4 - 7*x^3*y - 7*x^3 - x^2*y - 5*x^2 - 7*x*y - 3*x - 1)/((1 - x^6)*(1 - x^2*y^2)). - _J. Douglas Morrison_, Jul 24 2021
%e A132742 n\m|  0   1   2   3   4   5   6   7   8
%e A132742 ---+-----------------------------------
%e A132742 0  |  1
%e A132742 1  |  3   7
%e A132742 2  |  5   1   1
%e A132742 3  |  7   7   7   7
%e A132742 4  |  9   1   1   1   1
%e A132742 5  | 11   7   7   7   7   7
%e A132742 6  |  1   1   1   1   1   1   1
%e A132742 7  |  3   7   7   7   7   7   7   7
%e A132742 9  |  5   1   1   1   1   1   1   1   1
%e A132742 ...
%p A132742 a := (n, m) -> (1 + ((2*n*3^m) mod 12)): seq(seq(a(n, m), m = 0 .. n), n = 0 .. 20) # _Stefano Spezia_, Dec 26 2018
%t A132742 Flatten[Table[1 + Mod[2*n*3^m, 12], {n,0,20}, {m, 0, n}]] (* modified by _G. C. Greubel_, Feb 15 2021 *)
%o A132742 (GAP) Flat(List([0..20], n->List([0..n], m->(1 + ((2*n*3^m) mod 12))))); # _Stefano Spezia_, Dec 26 2018
%o A132742 (Magma) [([1 + ((2*n*3^k) mod 12): k in [0..n]]): n in [0..20]]; // _Stefano Spezia_, Dec 26 2018
%o A132742 (Maxima) sjoin(v, j) := apply(sconcat, rest(join(makelist(j, length(v)), v))); display_triangle(n) := for i from 0 thru n do disp(sjoin(makelist(1 + mod(2*i*3^j, 12), j, 0, i), " ")); display_triangle(20); /* _Stefano Spezia_, Dec 26 2018 */
%o A132742 (PARI) T(n, m) = 1 + ((2*n*3^m) % 12); \\ _Stefano Spezia_, Dec 26 2018
%o A132742 (Magma)
%o A132742 A132742:= func< n,k | 1 + ((2*n*3^k) mod 12) >;
%o A132742 [A132742(n,k): k in [0..n], n in [0..15]]; // _G. C. Greubel_, Feb 15 2021
%Y A132742 Cf. A000244, A005843.
%K A132742 nonn,tabl,less
%O A132742 0,2
%A A132742 _Roger L. Bagula_, Nov 17 2007
%E A132742 Edited by _Stefano Spezia_, Dec 26 2018