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Search: id:A129821
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| A129821 |
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Symmetric triangular sequence of powers: t(n,m)=m^n + (n - m)^n - n*m*(n - m). |
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+0
1
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| 1, 1, 1, 4, 0, 4, 27, 3, 3, 27, 256, 70, 16, 70, 256, 3125, 1005, 245, 245, 1005, 3125, 46656, 15596, 4112, 1404, 4112, 15596, 46656, 823543, 279895, 78183, 18487, 18487, 78183, 279895, 823543, 16777216, 5764746, 1679776, 397066, 130944, 397066
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Row sum: Table[Apply[Plus, Table[t[n, m], {n, 0, m}]], {m, 0, 10}]; {1, 2, 8, 60, 668, 8750, 134132, 2400216, 49368552, 1148608890, 29828682200} ( not in OEIS either) Inspired by the necklace law: f(x,y,q)=x+y-q*x*y (C. Lenart: the family of formal group laws over the integers F_q(X,Y)=X+Y-qXY, q in Z: http://math.albany.edu:8000/math/pers/lenart/articles/fgl.html)
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FORMULA
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t(n,m)=m^n + (n - m)^n - n*m*(n - m) else if n=m=0, 1
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EXAMPLE
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{1},
{1, 1},
{4, 0, 4},
{27, 3, 3, 27},
{256, 70, 16, 70, 256},
{3125, 1005, 245, 245, 1005, 3125},
{46656, 15596, 4112, 1404, 4112, 15596, 46656}
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MATHEMATICA
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t[m_, n_] = If [m == n == 0, 1, m^n + (n - m)^n - n*m*(n - m)]; aa = Table[Table[t[n, m], {n, 0, m}], {m, 0, 10}]; Flatten[aa]
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CROSSREFS
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Sequence in context: A087736 A005075 A103638 this_sequence A126836 A055241 A055242
Adjacent sequences: A129818 A129819 A129820 this_sequence A129822 A129823 A129824
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 08 2007
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