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1, 6, 13, 22, 33, 46, 61, 78, 97, 118, 141, 166, 193, 222, 253, 286, 321, 358, 397, 438, 481, 526, 573, 622, 673, 726, 781, 838, 897, 958, 1021, 1086, 1153, 1222, 1293, 1366, 1441, 1518, 1597, 1678, 1761, 1846, 1933, 2022, 2113, 2206, 2301
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OFFSET
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2,2
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COMMENTS
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Number of edges in the join of two star graphs, each of order n, S_n * S_n - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002
Sequence allows us to find X values of the equation: X^3 + (X - 3)^2 + X - 6 = Y^2. To prove that X = n^2 + 4n + 1: Y^2 = X^3 + (X - 3)^2 + X - 6 = X^3 + X^2 - 5X + 3 = (X + 3)(X^2 - 2X + 1) = (X + 3)*(X - 1)^2 it means: X = 1 or (X + 3) must be a perfect square, so X = k^2 - 3 with k>=2. we can put: k = n + 2, which gives: X = n^2 + 4n + 1 and Y = (n + 2)(n^2 + 4n). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 29 2007
Equals binomial transform of [1, 5, 2, 0, 0, 0,...] - Gary W. Adamson, Apr 30 2008
Let C = 2 + sqrt(3) = 3.732...; and 1/C = .267...; then a(n) = (n - 2 + C) * (n - 2 + 1/C). Example: a(5) = 46 = (5 + 3.732...)*(5 + .267...). - Gary W. Adamson, Jul 29 2009
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LINKS
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Table of n, a(n) for n=2..48.
P. De Geest, Palindromic Quasipronics of the form n(n+x)
Eric Weisstein's World of Mathematics, Near-Square Prime
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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O.g.f.: x^2*(-1-3*x+2*x^2)/(-1+x)^3. a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - R. J. Mathar, Apr 28 2008
a(n) = floor((n^4+2*n^3)/(n^2+1)). - Gary Detlefs, Feb 20 2010
a(n) = a(n-1)+2*n-1 (with a(2)=1). - Vincenzo Librandi, Nov 18 2010
a(n)*a(n-1)+3 = (a(n)-n)^2 = A014209(n-2)^2. - Bruno Berselli, Dec 07 2011
a(2)=1, a(3)=6, a(4)=13, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, May 09 2013
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MAPLE
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A028872 := proc(n) n^2-3; end proc: # R. J. Mathar, Aug 23 2011
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MATHEMATICA
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lst={}; Do[AppendTo[lst, n^2-3], {n, 6!}]; lst [From Vladimir Joseph Stephan Orlovsky, Jan 27 2009]
s = 1; lst = {s}; Do[s += n; AppendTo[lst, s], {n, 5, 100, 2}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]
Range[2, 60]^2-3 (* or *) LinearRecurrence[{3, -3, 1}, {1, 6, 13}, 60] (* Harvey P. Dale, May 09 2013 *)
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PROG
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(Sage) [lucas_number1(3, n, 3) for n in xrange(2, 50)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 03 2008
(PARI) a(n)=n^2-3 \\ _Charles R Greathouse_ IV, Aug 23 2011
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CROSSREFS
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Cf. A117950, A132411, A132414, A002522.
Sequence in context: A173358 A101247 A072212 * A049718 A036707 A054311
Adjacent sequences: A028869 A028870 A028871 * A028873 A028874 A028875
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KEYWORD
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nonn,easy,changed
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AUTHOR
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Patrick De Geest
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STATUS
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approved
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