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A185039
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Numbers of the form 9*m^2 + 4*m, m an integer.
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9
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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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).
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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.
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KEYWORD
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nonn,easy
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AUTHOR
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_N. J. A. Sloane_, Feb 04 2012
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STATUS
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approved
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