A130762 A fold back triangular sequence for A003991: symmetrical folding and addition of.

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, 20, 36, 48, 56, 60, 22, 40, 54, 64, 70, 36, 24, 44, 60, 72, 80, 84, 26, 48, 66, 80, 90, 96, 49, 28, 52, 72, 88, 100, 108, 112, 30, 56, 78, 96, 110, 120, 126, 64, 32, 60, 84, 104, 120

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..69.

Formula

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.

Example

{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},
{20, 36, 48, 56, 60},
{22, 40, 54, 64, 70, 36},
{24, 44, 60, 72, 80, 84}

Mathematica

(* 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[%]

Crossrefs

Cf. A000292, A003991.

Sequence in context: A018835 A055166 A202243 * A054002 A010300 A113209

Adjacent sequences: A130759 A130760 A130761 * A130763 A130764 A130765

Keyword

nonn,tabf,uned

Author

Roger L. Bagula, Jul 13 2007

Status

approved