A132728 Triangle T(n, k) = 4 - 3*(-1)^k, read by rows.
1, 1, 7, 1, 7, 1, 1, 7, 1, 7, 1, 7, 1, 7, 1, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1
Offset: 0
Examples
Triangle begins as: 1; 1, 7; 1, 7, 1; 1, 7, 1, 7; 1, 7, 1, 7, 1; 1, 7, 1, 7, 1, 7; 1, 7, 1, 7, 1, 7, 1; 1, 7, 1, 7, 1, 7, 1, 7; 1, 7, 1, 7, 1, 7, 1, 7, 1; 1, 7, 1, 7, 1, 7, 1, 7, 1, 7; 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1;
Links
- G. C. Greubel, Rows n = 0..30 of the triangle, flattened
Programs
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Magma
[4 -3*(-1)^k: k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 14 2021
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Mathematica
Table[PadRight[{},n,{1,7}],{n,20}]//Flatten (* Harvey P. Dale, Aug 02 2019 *) Table[4 -3*(-1)^k, {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, Feb 14 2021 *) -
Sage
flatten([[4 -3*(-1)^k for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 14 2021
Formula
From G. C. Greubel, Feb 14 2021: (Start)
T(n, k) = 4 - 3*(-1)^k.
Sum_{k=0..n} T(n, k) = (8*n + 5 - 3*(-1)^n)/2 = A047393(n+2). (End)
Bivariate g.f.: (1 + 7*x*y)/((1 - x)*(1 - x*y)*(1 + x*y)). - J. Douglas Morrison, Jul 19 2021
Extensions
Edited and corrected by Joerg Arndt, Dec 26 2018
Offset and title changed by G. C. Greubel, Feb 14 2021