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A155757
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(n^3 - n + 15)/3.
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1
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5, 7, 13, 25, 45, 75, 117, 173, 245, 335, 445, 577, 733, 915, 1125, 1365, 1637, 1943, 2285, 2665, 3085, 3547, 4053, 4605, 5205, 5855, 6557, 7313, 8125, 8995, 9925, 10917, 11973, 13095, 14285, 15545, 16877, 18283, 19765, 21325, 22965
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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)=5.
a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) = 5+n(n^2-1)/3 = 5+A007290(n+1). G.f.: x(5-13x+15x^2-5x^3)/(1-x)^4. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 19 2009]
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MATHEMATICA
| RecurrenceTable[{a[1]==5, a[n]==n(n-1)+a[n-1]}, a[n], {n, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {5, 7, 13, 25}, 50] (* From Harvey P. Dale, Jun 29 2011 *)
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PROG
| (PARI) a(n)=(n^3-n)/3+5 \\ Charles R Greathouse IV, Jan 11 2012
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CROSSREFS
| Sequence in context: A201474 A078724 A191022 * A027674 A124307 A158294
Adjacent sequences: A155754 A155755 A155756 * A155758 A155759 A155760
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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
| New name from Charles R Greathouse IV, Jan 11 2012
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