A176224 A symmetrical triangle sequence: T(n, k) = q^k + q^(n-k) - q^n, with q=2.

1, 1, 1, 1, 0, 1, 1, -2, -2, 1, 1, -6, -8, -6, 1, 1, -14, -20, -20, -14, 1, 1, -30, -44, -48, -44, -30, 1, 1, -62, -92, -104, -104, -92, -62, 1, 1, -126, -188, -216, -224, -216, -188, -126, 1, 1, -254, -380, -440, -464, -464, -440, -380, -254, 1

Offset

0,8

Comments

Row sums are: {1, 2, 2, -2, -18, -66, -194, -514, -1282, -3074, -7170, ...}.

Links

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

Formula

T(n,k) = q^k + q^(n-k) - q^n, with q = 2.

Example

Triangle begins as:
  1;
  1,    1;
  1,    0,    1;
  1,   -2,   -2,    1;
  1,   -6,   -8,   -6,    1;
  1,  -14,  -20,  -20,  -14,    1;
  1,  -30,  -44,  -48,  -44,  -30,    1;
  1,  -62,  -92, -104, -104,  -92,  -62,    1;
  1, -126, -188, -216, -224, -216, -188, -126,    1;
  1, -254, -380, -440, -464, -464, -440, -380, -254,    1;
  1, -510, -764, -888, -944, -960, -944, -888, -764, -510, 1;

Maple

q:=2; 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, 2], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Nov 23 2019 *)

Prog

(PARI) T(n, k, q) = my(q=2); q^k +q^(n-k) -q^n; \\ G. C. Greubel, Nov 23 2019
(Magma) q:=2; [q^k +q^(n-k) -q^n : k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 23 2019
(Sage) q=2; [[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:=2;; Flat(List([0..12], n-> List([0..n], k-> q^k +q^(n-k) -q^n ))); # G. C. Greubel, Nov 23 2019

Crossrefs

Cf. this sequence (q=2), A176225 (q=3), A176226 (q=5), A176227 (q=4).

Sequence in context: A127452 A263755 A135879 * A174640 A138169 A139331

Adjacent sequences: A176221 A176222 A176223 * A176225 A176226 A176227

Keyword

sign,tabl

Author

Roger L. Bagula, Apr 12 2010

Extensions

Edited by G. C. Greubel, Nov 23 2019

Status

approved