|
%I #7 Sep 08 2022 08:45:52
%S 1,1,1,1,-3,1,1,-15,-15,1,1,-51,-63,-51,1,1,-159,-207,-207,-159,1,1,
%T -483,-639,-675,-639,-483,1,1,-1455,-1935,-2079,-2079,-1935,-1455,1,1,
%U -4371,-5823,-6291,-6399,-6291,-5823,-4371,1,1,-13119,-17487,-18927,-19359,-19359,-18927,-17487,-13119,1
%N A symmetrical triangle sequence: T(n, k) = q^k + q^(n-k) - q^n, with q=3.
%C Row sums are: {1, 2, -1, -28, -163, -730, -2917, -10936, -39367, -137782, -472393, ...}.
%H G. C. Greubel, <a href="/A176225/b176225.txt">Rows n = 0..100 of triangle, flattened</a>
%F T(n,k) = q^k + q^(n-k) - q^n, with q = 3.
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, -3, 1;
%e 1, -15, -15, 1;
%e 1, -51, -63, -51, 1;
%e 1, -159, -207, -207, -159, 1;
%e 1, -483, -639, -675, -639, -483, 1;
%e 1, -1455, -1935, -2079, -2079, -1935, -1455, 1;
%e 1, -4371, -5823, -6291, -6399, -6291, -5823, -4371, 1;
%p q:=3; seq(seq(q^k +q^(n-k) -q^n, k=0..n), n=0..12); # _G. C. Greubel_, Nov 23 2019
%t T[n_, k_, q_]:= q^k +q^(n-k) -q^n; Table[T[n, k, 3], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by _G. C. Greubel_, Nov 23 2019 *)
%o (PARI) T(n,k,q) = my(q=3); q^k +q^(n-k) -q^n; \\ _G. C. Greubel_, Nov 23 2019
%o (Magma) q:=3; [q^k +q^(n-k) -q^n : k in [0..n], n in [0..12]]; // _G. C. Greubel_, Nov 23 2019
%o (Sage) q=3; [[q^k +q^(n-k) -q^n for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Nov 23 2019
%o (GAP) q:=3;; Flat(List([0..12], n-> List([0..n], k-> q^k +q^(n-k) -q^n ))); # _G. C. Greubel_, Nov 23 2019
%Y Cf. A176224 (q=2), this sequence (q=3), A176226 (q=5), A176227 (q=4).
%K sign,tabl
%O 0,5
%A _Roger L. Bagula_, Apr 12 2010
%E Edited by _G. C. Greubel_, Nov 23 2019
|
