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

0,2

Comments

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

Links

Stefano Spezia, First 150 rows of the triangle, flattened

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

Example

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
...

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 *)

Prog

(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
(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
(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

Crossrefs

Cf. A000244, A005843.

Sequence in context: A096627 A065084 A338769 * A267317 A210641 A021910

Adjacent sequences: A132739 A132740 A132741 * A132743 A132744 A132745

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Nov 17 2007

Extensions

Edited by Stefano Spezia, Dec 26 2018

Status

approved