|
%I #16 Feb 03 2023 07:18:20
%S 1,0,2,-1,2,2,-2,2,2,2,-3,2,2,2,2,-4,2,2,2,2,2,-5,2,2,2,2,2,2,-6,2,2,
%T 2,2,2,2,2,-7,2,2,2,2,2,2,2,2,-8,2,2,2,2,2,2,2,2,2,-9,2,2,2,2,2,2,2,2,
%U 2,2,-10,2,2,2,2,2,2,2,2,2,2,2,-11,2,2,2,2,2,2,2,2,2,2,2,2
%N Triangle T(n, k) = 1-n if k=0 else 2, read by rows.
%H G. C. Greubel, <a href="/A155124/b155124.txt">Rows n = 0..50 of the triangle, flattened</a>
%F From _G. C. Greubel_, Mar 25 2021: (Start)
%F T(n, k) = 1-n if k=0 else 2.
%F Sum_{k=0..n} T(n ,k) = n+1 = A000027(n+1). (End)
%e Triangle begins as:
%e 1;
%e 0, 2;
%e -1, 2, 2;
%e -2, 2, 2, 2;
%e -3, 2, 2, 2, 2;
%e -4, 2, 2, 2, 2, 2;
%e -5, 2, 2, 2, 2, 2, 2;
%e -6, 2, 2, 2, 2, 2, 2, 2;
%e -7, 2, 2, 2, 2, 2, 2, 2, 2;
%e -8, 2, 2, 2, 2, 2, 2, 2, 2, 2;
%e -9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2;
%t Table[CoefficientList[-(m-1) + 2*x*(1-x^m)/(1-x), x], {m,0,15}]//Flatten
%t Table[If[k==0, 1-n, 2], {n,0,15}, {k,0,n}]//Flatten (* _G. C. Greubel_, Mar 25 2021 *)
%o (Magma) [k eq 0 select 1-n else 2: k in [0..n], n in [0..15]]; // _G. C. Greubel_, Mar 25 2021
%o (Sage) flatten([[1-n if k==0 else 2 for k in (0..n)] for n in (0..15)]) # _G. C. Greubel_, Mar 25 2021
%K sign,tabl,easy,less
%O 0,3
%A _Roger L. Bagula_, Jan 20 2009
%E Edited by _G. C. Greubel_, Mar 25 2021
|
