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A168281 Triangle T(n,m) = 2*(min(n - m + 1, m))^2 read by rows.

%I A168281 #24 Jul 25 2024 08:49:19
%S A168281 2,2,2,2,8,2,2,8,8,2,2,8,18,8,2,2,8,18,18,8,2,2,8,18,32,18,8,2,2,8,18,
%T A168281 32,32,18,8,2,2,8,18,32,50,32,18,8,2,2,8,18,32,50,50,32,18,8,2,2,8,18,
%U A168281 32,50,72,50,32,18,8,2,2,8,18,32,50,72,72,50,32,18,8,2,2,8,18,32,50,72,98,72
%N A168281 Triangle T(n,m) = 2*(min(n - m + 1, m))^2 read by rows.
%C A168281 Row sums are A099956(n-1) = 2*A005993(n-1).
%C A168281 The flattened triangle is simply 2 followed by A137508.
%C A168281 If A106314 is interpreted as a triangle, T(n,m) = 2*A106314(n,m).
%H A168281 Michael De Vlieger, <a href="/A168281/b168281.txt">Table of n, a(n) for n = 1..10011</a> (First 141 rows).
%e A168281 The table starts in row n=1 with columns 1<=m<=n as:
%e A168281   2;
%e A168281   2,2;
%e A168281   2,8,2;
%e A168281   2,8,8,2;
%e A168281   2,8,18,8,2;
%e A168281   2,8,18,18,8,2;
%e A168281   ...
%p A168281 A168281 := proc(n,m) 2*(min(n+1-m,m))^2 ; end proc:
%p A168281 seq(seq(A168281(n,m),m=1..n),n=1..20) ;
%t A168281 Table[Map[2 Min[n + # - 1, #]^2 &, Drop[#, -Boole@ EvenQ@ n] ~Join~ Reverse@ # &@ Range@ Floor[n/2]], {n, 2, 14}] // Flatten (* _Michael De Vlieger_, Jul 19 2016 *)
%Y A168281 Cf. A005993, A099956, A137508, A106314.
%K A168281 nonn,tabl,easy
%O A168281 1,1
%A A168281 _Paul Curtz_, Nov 22 2009
%E A168281 Rephrased all comments in terms of a triangle by _R. J. Mathar_, Nov 24 2010
%E A168281 More terms from _Michael De Vlieger_, Jul 19 2016
%E A168281 Definition corrected by _Georg Fischer_, Nov 11 2021