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A177071
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(7n + 3)(7n + 4).
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2
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12, 110, 306, 600, 992, 1482, 2070, 2756, 3540, 4422, 5402, 6480, 7656, 8930, 10302, 11772, 13340, 15006, 16770, 18632, 20592, 22650, 24806, 27060, 29412, 31862, 34410, 37056, 39800, 42642, 45582, 48620, 51756, 54990, 58322, 61752, 65280
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OFFSET
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0,1
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COMMENTS
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Cf. Zumkeller's contribution in A177059: in general, (h*n+h-k)*(h*n+k) = h^2*A002061(n+1)+(h-k)*k-h^2, therefore a(n) = 49*A002061(n+1)-37. [Bruno Berselli, Aug 24 2010]
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 98*n+a(n-1) with n>0, a(0)=12.
a(0)=12, a(1)=110, a(2)=306, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, Oct 09 2011]
G.f.: -((2*(x+6)*(6*x+1))/(x-1)^3) [From Harvey P. Dale, Oct 09 2011]
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MATHEMATICA
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Table[(7n+3)(7n+4), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {12, 110, 306}, 40] (* From Harvey P. Dale, Oct 09 2011 *)
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PROG
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(PARI) a(n)=2*binomial(7*n+4, 2) \\ Charles R Greathouse IV, Jan 11 2012
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CROSSREFS
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Sequence in context: A081200 A016214 A037581 * A081183 A069294 A000559
Adjacent sequences: A177068 A177069 A177070 * A177072 A177073 A177074
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, May 31 2010
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EXTENSIONS
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Edited by N. J. A. Sloane, Jun 22 2010
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STATUS
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approved
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