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 A280719 Expansion of (Sum_{k>=0} x^(k*(2*k-1)))^6. 2
 1, 6, 15, 20, 15, 6, 7, 30, 60, 60, 30, 6, 15, 60, 90, 66, 45, 60, 80, 90, 66, 50, 120, 180, 135, 60, 15, 60, 186, 210, 141, 126, 120, 126, 165, 180, 241, 300, 210, 90, 90, 180, 270, 270, 210, 212, 270, 270, 200, 210, 366, 450, 390, 270, 135, 210, 375, 360, 396, 420, 300, 330, 375, 380, 510, 480, 336, 450, 510, 390, 330 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of ways to write n as an ordered sum of 6 hexagonal numbers (A000384). a(n) > 0 for all n >= 0. Every number is the sum of at most 6 hexagonal numbers. Every number is the sum of at most k k-gonal numbers (Fermat's polygonal number theorem). LINKS Ilya Gutkovskiy, Extended graphical example Eric Weisstein's World of Mathematics, Hexagonal Number FORMULA G.f.: (Sum_{k>=0} x^(k*(2*k-1)))^6. EXAMPLE a(6) = 7 because we have: [6, 0, 0, 0, 0, 0] [0, 6, 0, 0, 0, 0] [0, 0, 6, 0, 0, 0] [0, 0, 0, 6, 0, 0] [0, 0, 0, 0, 6, 0] [0, 0, 0, 0, 0, 6] [1, 1, 1, 1, 1, 1] MATHEMATICA nmax = 70; CoefficientList[Series[Sum[x^(k (2 k - 1)), {k, 0, nmax}]^6, {x, 0, nmax}], x] CROSSREFS Cf. A000384, A007536, A008440, A045848, A280718, A282248. Sequence in context: A063266 A131892 A291381 * A282173 A045848 A294651 Adjacent sequences:  A280716 A280717 A280718 * A280720 A280721 A280722 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Feb 10 2017 STATUS approved

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Last modified August 21 06:54 EDT 2019. Contains 326162 sequences. (Running on oeis4.)