OFFSET
0,3
LINKS
G. C. Greubel, Rows n = 0..30 of the triangle, flattened
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
EXAMPLE
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;
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 *)
PROG
(Sage) flatten([[4 -3*(-1)^k for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 14 2021
(Magma) [4 -3*(-1)^k: k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 14 2021
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Nov 17 2007
EXTENSIONS
Edited and corrected by Joerg Arndt, Dec 26 2018
Offset and title changed by G. C. Greubel, Feb 14 2021
STATUS
approved