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A130762
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A fold back triangular sequence for A003991: symmetrical folding and addition of.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sum is still A000292. These sequences are relate 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.
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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.
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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}
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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[%]
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CROSSREFS
| Cf. A000292, A003991.
Sequence in context: A018835 A055166 A202243 * A054002 A010300 A113209
Adjacent sequences: A130759 A130760 A130761 * A130763 A130764 A130765
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KEYWORD
| nonn,tabf,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jul 13 2007
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