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 A162499 Triangle read by rows in which row n gives coefficients of the expansion of the polynomial Product( (1-x^(3*k))/(1-x), k=1..n). 31
 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 2, 1, 1, 3, 6, 9, 12, 15, 17, 18, 18, 17, 15, 12, 9, 6, 3, 1, 1, 4, 10, 19, 31, 46, 63, 81, 99, 116, 131, 143, 151, 154, 151, 143, 131, 116, 99, 81, 63, 46, 31, 19, 10, 4, 1, 1, 5, 15, 34, 65, 111, 174, 255, 354, 470, 601, 744, 895 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 REFERENCES A. V. Yurkin, New binomial and new view on light theory, (book), 2013, 78 pages, no publisher listed. LINKS G. C. Greubel, Rows n=0..20 of triangle, flattened A. V. Yurkin, On similarity of systems of geometrical and arithmetic triangles, in Mathematics, Computing, Education Conference XIX, 2012. A. V. Yurkin, New view on the diffraction discovered by Grimaldi and Gaussian beams, arXiv:1302.6287 [physics.optics], 2013. EXAMPLE Triangle begins: 1 1, 1, 1 1, 2, 3, 3, 3, 3, 2, 1, 1, 3, 6, 9, 12, 15, 17, 18, 18, 17, 15, 12, 9, 6, 3, 1, 1, 4, 10, 19, 31, 46, 63, 81, 99, 116, 131, 143, 151, 154, 151, 143, 131, 116, 99, 81, 63, 46, 31, 19, 10, 4, 1 1, 5, 15, 34, 65, 111, 174, 255, 354, 470, 601, 744, 895, 1049, 1200, 1342, 1469, 1575, 1655, 1705, 1722, 1705, 1655, 1575, 1469, 1342, 1200, 1049, 895, 744, 601, 470, 354, 255, 174, 111, 65, 34, 15, 5, 1, ... MATHEMATICA row[n_] := CoefficientList[Product[(1 - x^(3*k))/(1 - x), {k, 1, n}], x]; Table[row[n], {n, 0, 5}] // Flatten (* Jean-François Alcover, Sep 19 2016 *) CROSSREFS Rows give A162500, ... Sequence in context: A127661 A358617 A008968 * A350857 A135715 A089326 Adjacent sequences: A162496 A162497 A162498 * A162500 A162501 A162502 KEYWORD nonn,tabf,look AUTHOR N. J. A. Sloane, Dec 02 2009 STATUS approved

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Last modified November 30 21:57 EST 2022. Contains 358453 sequences. (Running on oeis4.)