A176227 A symmetrical triangle sequence: T(n, k) = q^k + q^(n-k) - q^n, with q=4.

1, 1, 1, 1, -8, 1, 1, -44, -44, 1, 1, -188, -224, -188, 1, 1, -764, -944, -944, -764, 1, 1, -3068, -3824, -3968, -3824, -3068, 1, 1, -12284, -15344, -16064, -16064, -15344, -12284, 1, 1, -49148, -61424, -64448, -65024, -64448, -61424, -49148, 1

Offset

0,5

Comments

Row sums are: {1, 2, -6, -86, -598, -3414, -17750, -87382, -415062, -1922390, -8738134, ...}.

Links

G. C. Greubel, Rows n = 0..100 of triangle, flattened

Formula

T(n,k) = q^k + q^(n-k) - q^n, with q = 4.

Example

Triangle begins as:
  1;
  1,      1;
  1,     -8,      1;
  1,    -44,    -44,      1;
  1,   -188,   -224,   -188,      1;
  1,   -764,   -944,   -944,   -764,      1;
  1,  -3068,  -3824,  -3968,  -3824,  -3068,      1;
  1, -12284, -15344, -16064, -16064, -15344, -12284, 1;

Maple

q:=4; seq(seq(q^k +q^(n-k) -q^n, k=0..n), n=0..12); # G. C. Greubel, Nov 23 2019

Mathematica

T[n_, k_, q_]:= q^k +q^(n-k) -q^n; Table[T[n, k, 4], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Nov 23 2019 *)

Prog

(PARI) T(n, k, q) = my(q=4); q^k +q^(n-k) -q^n; \\ G. C. Greubel, Nov 23 2019
(Magma) q:=4; [q^k +q^(n-k) -q^n : k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 23 2019
(Sage) q=4; [[q^k +q^(n-k) -q^n for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 23 2019
(GAP) q:=4;; Flat(List([0..12], n-> List([0..n], k-> q^k +q^(n-k) -q^n ))); # G. C. Greubel, Nov 23 2019

Crossrefs

Cf. A176224 (q=2), A176225 (q=3), A176226 (q=5), this sequence (q=4).

Sequence in context: A142458 A174528 A259465 * A340560 A022171 A203443

Adjacent sequences: A176224 A176225 A176226 * A176228 A176229 A176230

Keyword

sign,tabl

Author

Roger L. Bagula, Apr 12 2010

Extensions

Edited by G. C. Greubel, Nov 23 2019

Status

approved