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).
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
KEYWORD
AUTHOR
Roger L. Bagula, Nov 17 2007
EXTENSIONS
Edited by Stefano Spezia, Dec 26 2018
STATUS
approved