A176227 - OEIS

%I #6 Sep 08 2022 08:45:52

%S 1,1,1,1,-8,1,1,-44,-44,1,1,-188,-224,-188,1,1,-764,-944,-944,-764,1,

%T 1,-3068,-3824,-3968,-3824,-3068,1,1,-12284,-15344,-16064,-16064,

%U -15344,-12284,1,1,-49148,-61424,-64448,-65024,-64448,-61424,-49148,1

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

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

%H G. C. Greubel, <a href="/A176227/b176227.txt">Rows n = 0..100 of triangle, flattened</a>

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

%e Triangle begins as:

%e   1;

%e   1,      1;

%e   1,     -8,      1;

%e   1,    -44,    -44,      1;

%e   1,   -188,   -224,   -188,      1;

%e   1,   -764,   -944,   -944,   -764,      1;

%e   1,  -3068,  -3824,  -3968,  -3824,  -3068,      1;

%e   1, -12284, -15344, -16064, -16064, -15344, -12284, 1;

%p q:=4; 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, 4], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by _G. C. Greubel_, Nov 23 2019 *)

%o (PARI) T(n,k,q) = my(q=4); q^k +q^(n-k) -q^n; \\ _G. C. Greubel_, Nov 23 2019

%o (Magma) q:=4; [q^k +q^(n-k) -q^n : k in [0..n], n in [0..12]]; // _G. C. Greubel_, Nov 23 2019

%o (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

%o (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

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

%K sign,tabl

%O 0,5

%A _Roger L. Bagula_, Apr 12 2010

%E Edited by _G. C. Greubel_, Nov 23 2019