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A176224
A symmetrical triangle sequence: T(n, k) = q^k + q^(n-k) - q^n, with q=2.
4
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, ...}.
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
KEYWORD
sign,tabl
AUTHOR
Roger L. Bagula, Apr 12 2010
EXTENSIONS
Edited by G. C. Greubel, Nov 23 2019
STATUS
approved