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A082109
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Third row of number array A082105.
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8
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1, 13, 33, 61, 97, 141, 193, 253, 321, 397, 481, 573, 673, 781, 897, 1021, 1153, 1293, 1441, 1597, 1761, 1933, 2113, 2301, 2497, 2701, 2913, 3133, 3361, 3597, 3841, 4093, 4353, 4621, 4897, 5181, 5473, 5773, 6081, 6397, 6721, 7053, 7393, 7741, 8097, 8461
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OFFSET
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0,2
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COMMENTS
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Define b(n)=A000217(n), the triangular numbers. Using six consecutive terms to create the vertices of a triangle at points (b(n-2),b(n-1)), (b(n),b(n+1)), and (b(n+2),b(n+3)), one fourth the area of these triangles = a(n). - J. M. Bergot, Jul 30 2013
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LINKS
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Table of n, a(n) for n=0..45.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1)
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FORMULA
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a(n) = 4n^2 + 8n + 1.
a(n) = 8*n + a(n-1) + 4 (with a(0)=1). - Vincenzo Librandi, Aug 08 2010
G.f.: (1 + 10*x - 3*x^2)/(1-x)^3. - Bruno Berselli, Apr 18 2011
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EXAMPLE
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a(1)=8*1+1+4=13; a(2)=8*2+13+4=33; a(3)=8*3+33+4=61. - Vincenzo Librandi, Aug 08 2010
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MATHEMATICA
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s=-3; lst={}; Do[s+=n+1; AppendTo[lst, s], {n, 3, 6!, 8}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 25 2008 *)
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PROG
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(PARI) a(n)=4*n^2+8*n+1 \\ Charles R Greathouse IV, Jun 17 2017
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CROSSREFS
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Cf. A082108.
Column 2 of array A188646.
Sequence in context: A050659 A123161 A146052 * A024839 A146177 A146194
Adjacent sequences: A082106 A082107 A082108 * A082110 A082111 A082112
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Apr 03 2003
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STATUS
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approved
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