A130762 - OEIS

%I #5 Apr 14 2013 02:26:27

%S 1,4,6,4,8,12,10,16,9,12,20,24,14,24,30,16,16,28,36,40,18,32,42,48,25,

%T 20,36,48,56,60,22,40,54,64,70,36,24,44,60,72,80,84,26,48,66,80,90,96,

%U 49,28,52,72,88,100,108,112,30,56,78,96,110,120,126,64,32,60,84,104,120

%N A fold back triangular sequence for A003991: symmetrical folding and addition of.

%C Row sum is still A000292. These sequences are related to heights of Cartan A_n groups. I spent half the night trying to get this algorithm to work and just barely got this to do what I was doing with ease by hand. The other fold back sequences were analogs for this.

%F a0(n,m) = (n-m)*(1+m) Doubling of all elements a(n,m)=2*a0(n,m)-> m->Floor[n/2] except for the uneven middle element on odd sequences in n.

%e {1},

%e {4},

%e {6, 4},

%e {8, 12},

%e {10, 16, 9},

%e {12, 20, 24},

%e {14, 24, 30, 16},

%e {16, 28, 36, 40},

%e {18, 32, 42, 48, 25},

%e {20, 36, 48, 56, 60},

%e {22, 40, 54, 64, 70, 36},

%e {24, 44, 60, 72, 80, 84}

%t (* first A003991*) a = Table[Table[(n - i)*(1 + i), {i, 0, n - 1}], {n, 1, 20}]; (* then fold back from that*) Table[Table[If[ Mod[n, 2] == 1, a[[n]][[m]] + a[[n]][[Length[a[[n]]] - m]] - n, If[m - Floor[ n/2] == 0, (a[[n]][[m]] + a[[ n]][[Length[a[[n]]] - m]] - n)/ 2, a[[n]][[m]] + a[[n]][[Length[a[[n]]] - m]] - n]], {m, 1, Floor[n/ 2]}], {n, 1, Length[a]}]; Flatten[%]

%Y Cf. A000292, A003991.

%K nonn,tabf,uned

%O 1,2

%A _Roger L. Bagula_, Jul 13 2007