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
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
Programs
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GAP
Flat(List([0..20], n->List([0..n], m->(1 + ((2*n*3^m) mod 12))))); # Stefano Spezia, Dec 26 2018
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Magma
[([1 + ((2*n*3^k) mod 12): k in [0..n]]): n in [0..20]]; // Stefano Spezia, Dec 26 2018
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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
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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
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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 */
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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).
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
Comments