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 A176646 a(n) = 12*n^5 + 25*n^4 + 5*n^3 - 10*n^2 - 2*n. 1
 0, 30, 780, 4980, 18840, 53490, 126420, 262920, 497520, 875430, 1453980, 2304060, 3511560, 5178810, 7426020, 10392720, 14239200, 19147950, 25325100, 33001860, 42435960, 53913090, 67748340, 84287640, 103909200, 127024950, 154081980, 185563980, 221992680, 263929290, 311975940, 366777120, 429021120, 499441470, 578818380, 667980180, 767804760, 879221010 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Appears in Theorem 2.1, p.2 of Zhu. Zhu writes that the number P(n) of convex pentagons in an n-triangular net is 12*k^5 + 25*k^4 + 5*k^3 - 10*k^2 - 2*k, for n = 2*k + 1 (k = 0, 1, 2, ...) and a different formula for n even [this being a polynomial in k, and another formula for n, rather than a polynomial in n as given in this OEIS sequence]. LINKS Jun-Ming Zhu, The number of convex pentagons and hexagons in an n-triangular net, arXiv:1012.4058 [math.CO], 2010. Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1) FORMULA G.f.: 30*x*(1 + 20*x + 25*x^2 + 2*x^3)/(x-1)^6. a(n) = n*(n+1)*(12*n^3 + 13*n^2 - 8*n - 2). EXAMPLE a(4) = (12*(4^5) + 25*(4^4) + 5*(4^3) - 10*(4^2) - 2*4) = 18840 = 2^3*3*5*157. MAPLE A176646 := proc(n)12*n^5 + 25*n^4 + 5*n^3 - 10*n^2 - 2*n ; end proc: seq(A176646(n), n=0..40) ; # R. J. Mathar, Dec 21 2010 MATHEMATICA LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 30, 780, 4980, 18840, 53490}, 40] (* Harvey P. Dale, Jan 14 2015 *) CROSSREFS Sequence in context: A045689 A096722 A261030 * A160269 A049394 A143169 Adjacent sequences:  A176643 A176644 A176645 * A176647 A176648 A176649 KEYWORD nonn,easy AUTHOR Jonathan Vos Post, Dec 21 2010 STATUS approved

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Last modified May 13 10:40 EDT 2021. Contains 343839 sequences. (Running on oeis4.)