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0, 4, 10, 18, 28, 40, 54, 70, 88, 108, 130, 154, 180, 208, 238, 270, 304, 340, 378, 418, 460, 504, 550, 598, 648, 700, 754, 810, 868, 928, 990, 1054, 1120, 1188, 1258, 1330, 1404, 1480, 1558, 1638, 1720, 1804, 1890, 1978, 2068
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| n(n-3) (n >= 3) is the number of [body] diagonals of an n-gonal prism - Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr).
a(n) = A028387(n)-1. Half of the difference between n(n+1)(n+2)(n+3) and the largest square less than it. Calling this difference "SquareMod": a(n) = (1/2)*SqareMod(n(n+1)(n+2)(n+3)). - Rainer Rosenthal (r.rosenthal(AT)web.de), Sep 04 2004
n != -2 such that x^4 + x^3 - n*x^2 + x + 1 is reducible over the integers. Starting at 10: n such that x^4 + x^3 - n*x^2 + x + 1 is a product of irreducible quadratic factors over the integers. - James Buddenhagen (jbuddenh(AT)gmail.com), Apr 19 2005
If a 3-set Y and a 3-set Z, having two element in common, are subsets of an n-set X then a(n-4) is the number of 3-subests of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Oct 03 2007
Starting with offset 1 = binomial transform of [4, 6, 2, 0, 0, 0,...] [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 09 2009]
a(A002522(n)) = A156798(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 16 2009]
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LINKS
| Milan Janjic, Two Enumerative Functions
P. De Geest, Palindromic Quasipronics of the form n(n+x)
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n)=2*n+a(n-1)+2 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 05 2010]
sum_{n>=1} 1/a(n) = 11/18 via sum_{n>=0} 1/(n+x)/(n+y) = (psi(x)-psi(y))/(x-y). - R. J. Mathar, Mar 22 2011
G.f.: 2*x*(2 - x)/(1 - x)^3. [Arkadiusz Wesolowski, Dec 31 2011]
a(0)=0, a(1)=4, a(2)=10, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, Feb 05 2012]
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MAPLE
| A028552 := proc(n) n*(n+3); end proc: - R. J. Mathar, Jan 29 2011
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MATHEMATICA
| lst={}; Do[AppendTo[lst, n*(n+3)], {n, 0, 6!, 1}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 07 2008]
LinearRecurrence[{3, -3, 1}, {0, 4, 10}, 50] (* From Harvey P. Dale, Feb 05 2012 *)
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PROG
| (MAGMA) [n*(n+3): n in [0..150] ]; // Vincenzo Librandi, Apr 21 2011
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CROSSREFS
| Cf. A028387, A062145, A002522.
Sequence in context: A009876 A161958 A013921 * A009877 A009880 A197057
Adjacent sequences: A028549 A028550 A028551 * A028553 A028554 A028555
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KEYWORD
| nonn,easy,nice,changed
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AUTHOR
| Patrick De Geest (pdg(AT)worldofnumbers.com)
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