|
%I #6 Sep 08 2022 08:45:52
%S 1,1,1,1,-15,1,1,-95,-95,1,1,-495,-575,-495,1,1,-2495,-2975,-2975,
%T -2495,1,1,-12495,-14975,-15375,-14975,-12495,1,1,-62495,-74975,
%U -77375,-77375,-74975,-62495,1,1,-312495,-374975,-387375,-389375,-387375,-374975,-312495,1
%N A symmetrical triangle sequence: T(n, k) = q^k + q^(n-k) - q^n, with q=5.
%C Row sums are: {1, 2, -13, -188, -1563, -10938, -70313, -429688, -2539063, -14648438, -83007813, ...}.
%H G. C. Greubel, <a href="/A176226/b176226.txt">Rows n = 0..100 of triangle, flattened</a>
%F T(n,k) = q^k + q^(n-k) - q^n, with q = 5.
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, -15, 1;
%e 1, -95, -95, 1;
%e 1, -495, -575, -495, 1;
%e 1, -2495, -2975, -2975, -2495, 1;
%e 1, -12495, -14975, -15375, -14975, -12495, 1; 1, -62495, -74975, -77375, -77375, -74975, -62495, 1;
%p q:=5; 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, 5], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by _G. C. Greubel_, Nov 23 2019 *)
%o (PARI) T(n,k,q) = my(q=5); q^k +q^(n-k) -q^n; \\ _G. C. Greubel_, Nov 23 2019
%o (Magma) q:=5; [q^k +q^(n-k) -q^n : k in [0..n], n in [0..12]]; // _G. C. Greubel_, Nov 23 2019
%o (Sage) q=5; [[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:=5;; 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), this sequence (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
|
