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A109439
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Triangle read by rows, in which row n gives coefficients in expansion of ((1 - x^n)/(1 - x))^3.
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1
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1, 1, 3, 3, 1, 1, 3, 6, 7, 6, 3, 1, 1, 3, 6, 10, 12, 12, 10, 6, 3, 1, 1, 3, 6, 10, 15, 18, 19, 18, 15, 10, 6, 3, 1, 1, 3, 6, 10, 15, 21, 25, 27, 27, 25, 21, 15, 10, 6, 3, 1, 1, 3, 6, 10, 15, 21, 28, 33, 36, 37, 36, 33, 28, 21, 15, 10, 6, 3, 1, 1, 3, 6, 10, 15, 21, 28, 36, 42, 46, 48, 48
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OFFSET
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0,3
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COMMENTS
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Sum in n-th row is (n+1)^3. The n-th row includes 3n+1 entries. Largest coefficients in rows are listed in A077043. The 255-th row describes distribution of color lattice points in the 765 r+g+b=k planes of 24 bitRGB-cube with 256^3 points.
The number of cubes 1 X 1 X 1 used to build a cube by layers perpendicular to the great diagonal. Each layer is made of regular triangular numbers T near the summits and truncated T's in the middle. E.g. cube 3^3 is made of layers 1, 3, 6, 7, 6, 3, 1, using T1, T2, T3 and a regularly truncated T4, 7 instead of 10. - M. Dauchez (mdzzdm(AT)yahoo.fr), Aug 31 2005
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LINKS
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Table of n, a(n) for n=0..81.
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EXAMPLE
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The 0-th to 3rd rows are
1;
1, 3, 3, 1;
1, 3, 6, 7, 6, 3, 1;
1,3,6,10,12,12,10,6,3,1;
The 5th row is: {1,3,6,10,15,21,25,27,27,25,21,15,10,6,3,1}.
Sum of 5-th row is 216=(5+1)^3=216.
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MATHEMATICA
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Flatten[Table[CoefficientList[Series[((1-x^n)/(1-x))^3, {x, 1, 3*n}], x], {n, 1, 100}], 1]
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CROSSREFS
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Cf. A000217, A077043, A045943.
Sequence in context: A090569 A160324 A197928 * A133333 A171876 A133332
Adjacent sequences: A109436 A109437 A109438 * A109440 A109441 A109442
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KEYWORD
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nonn,tabf
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 30 2005
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STATUS
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approved
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