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 A185039 Numbers of the form 9*m^2 + 4*m, m an integer. 9
 0, 5, 13, 28, 44, 69, 93, 128, 160, 205, 245, 300, 348, 413, 469, 544, 608, 693, 765, 860, 940, 1045, 1133, 1248, 1344, 1469, 1573, 1708, 1820, 1965, 2085, 2240, 2368, 2533, 2669, 2844, 2988, 3173, 3325, 3520, 3680, 3885, 4053, 4268, 4444, 4669, 4853, 5088 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also, numbers m such that 9*m+4 is a square. After 0, therefore, there are no squares in this sequence. - Bruno Berselli, Jan 07 2016 LINKS Bruno Berselli, Table of n, a(n) for n = 1..1000 S. Cooper and M. D. Hirschhorn, Results of Hurwitz type for three squares. Discrete Math. 274 (2004), no. 1-3, 9-24. See B(q). Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA From Bruno Berselli, Feb 04 2012: (Start) G.f.: x*(5+8*x+5*x^2)/((x+1)^2*(1-x)^3). a(n) = a(-n+1) = (18*n*(n-1)+(2*n-1)*(-1)^n+1)/8 = A004526(n)*A156638(n). (End). MATHEMATICA CoefficientList[Series[x*(5+8*x+5*x^2)/((x+1)^2*(1-x)^3), {x, 0, 50}], x] (* G. C. Greubel, Jun 20 2017 *) LinearRecurrence[{1, 2, -2, -1, 1}, {0, 5, 13, 28, 44}, 50] (* Harvey P. Dale, Jan 23 2018 *) PROG (MAGMA) [0] cat &cat[[9*n^2-4*n, 9*n^2+4*n]: n in [1..32]]; // Bruno Berselli, Feb 04 2011 (PARI) x='x+O('x^50); Vec(x*(5+8*x+5*x^2)/((x+1)^2*(1-x)^3)) \\ G. C. Greubel, Jun 20 2017 CROSSREFS Characteristic function is A205809. Numbers of the form 9*n^2+k*n, for integer n: A016766 (k=0), A132355 (k=2), this sequence (k=4), A057780 (k=6), A218864 (k=8). [Jason Kimberley, Nov 08 2012] For similar sequences of numbers m such that 9*m+k is a square, see list in A266956. Sequence in context: A296775 A272045 A248860 * A316537 A175254 A211636 Adjacent sequences:  A185036 A185037 A185038 * A185040 A185041 A185042 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Feb 04 2012 STATUS approved

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Last modified September 24 07:28 EDT 2020. Contains 337317 sequences. (Running on oeis4.)