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A155753
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(n^3 - n + 9)/3.
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1
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3, 5, 11, 23, 43, 73, 115, 171, 243, 333, 443, 575, 731, 913, 1123, 1363, 1635, 1941, 2283, 2663, 3083, 3545, 4051, 4603, 5203, 5853, 6555, 7311, 8123, 8993, 9923, 10915, 11971, 13093, 14283, 15543, 16875, 18281, 19763, 21323, 22963
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n)+a(n-1)=2*A153057(n-1) (n>1); a(n)+A000217(n)=A153057(n) (n>0). [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Jun 21 2010]
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LINKS
| B. Berselli, Table of n, a(n) for n = 1..10000.
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
| a(n)=n(n-1)+a(n-1), with a(1)=3 .
Contribution from Bruno Berselli (berselli.bruno(AT)yahoo.it), Jun 21 2010: (Start)
G.f.: x*(3-9*x+11*x^2-3*x^3)/(1-x)^4.
a(n)-4*a(n-1)+6*a(n-2)-4*a(n-3)+a(n-4) = 0 with n>4.
a(n) = 3+A007290(n+1) = (n^3-n+9)/3. (End)
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MATHEMATICA
| f[n_]:=(n^3 - n + 9)/3; f[Range[1, 100]] (*From Vladimir Joseph Stephan Orlovsky, Feb 10 2011*)
LinearRecurrence[{4, -6, 4, -1}, {3, 5, 11, 23}, 50] (* From Harvey P. Dale, Oct 20 2011 *)
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PROG
| (PARI) a(n)=(n^3-n)/3+3 \\ Charles R Greathouse IV, Jan 11 2012
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CROSSREFS
| Sequence in context: A056874 A109927 A146276 * A133914 A169913 A023223
Adjacent sequences: A155750 A155751 A155752 * A155754 A155755 A155756
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 26 2009
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EXTENSIONS
| Entries confirmed by John W. Layman, Jun 17 2010.
Edited by Bruno Berselli (berselli.bruno(AT)yahoo.it), Aug 12 2010
New name from Charles R Greathouse IV, Jan 11 2012
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