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

0,3

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

Cf. A010688, A047393, A132742.

Sequence in context: A322663 A231927 A199076 * A083530 A191562 A296472

Adjacent sequences: A132725 A132726 A132727 * A132729 A132730 A132731

Keyword

nonn,easy,tabl,less

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