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

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, 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, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Roger L. Bagula, Nov 17 2007

Keywords

• nonn
• tabl
• less

Comments

T(n,m) differs from A132728 in the order in which n and m are handled.

Examples

			n\m|  0   1   2   3   4   5   6   7   8
---+-----------------------------------
0  |  1
1  |  3   7
2  |  5   1   1
3  |  7   7   7   7
4  |  9   1   1   1   1
5  | 11   7   7   7   7   7
6  |  1   1   1   1   1   1   1
7  |  3   7   7   7   7   7   7   7
9  |  5   1   1   1   1   1   1   1   1
...
		

Links

• Stefano Spezia, First 150 rows of the triangle, flattened

Crossrefs

Cf. A000244, A005843.

Programs

GAP

Flat(List([0..20], n->List([0..n], m->(1 + ((2*n*3^m) mod 12))))); # Stefano Spezia, Dec 26 2018

Magma

[([1 + ((2*n*3^k) mod 12): k in [0..n]]): n in [0..20]]; // Stefano Spezia, Dec 26 2018

Magma

A132742:= func< n,k | 1 + ((2*n*3^k) mod 12) >;
[A132742(n,k): k in [0..n], n in [0..15]]; // G. C. Greubel, Feb 15 2021

Maple

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

Mathematica

Flatten[Table[1 + Mod[2*n*3^m, 12], {n,0,20}, {m, 0, n}]] (* modified by G. C. Greubel, Feb 15 2021 *)

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 */

PARI

T(n, m) = 1 + ((2*n*3^m) % 12); \\ Stefano Spezia, Dec 26 2018

Formula

T(n,m) = 1 + ((2*n*3^m) mod 12).

T(n,m) = 1 + ((A005843(n)*A000244(m)) mod 12). - Stefano Spezia, Dec 26 2018

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

Extensions

Edited by Stefano Spezia, Dec 26 2018