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0, 5, 14, 27, 44, 65, 90, 119, 152, 189, 230, 275, 324, 377, 434, 495, 560, 629, 702, 779, 860, 945, 1034, 1127, 1224, 1325, 1430, 1539, 1652, 1769, 1890, 2015, 2144, 2277, 2414, 2555, 2700, 2849, 3002, 3159, 3320, 3485, 3654, 3827, 4004, 4185, 4370
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| If Y is a 2-subset of a 2n-set X then, for n>=1, a(n-1) is the number of (2n-2)-subsets of X intersecting Y. - Milan R. Janjic (agnus(AT)blic.net), Nov 18 2007
This sequence can also be derived from 1*(2+3)=5, 2*(3+4)=14, 3*(4+5)=27, and so forth. [J. M Bergot, May 30 2011]
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REFERENCES
| Jolley, Summation of Series, Dover (1961).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..920
Milan Janjic, Two Enumerative Functions
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) -1 = A091823(n). - Howard A. Landman (howard(AT)riverrock.org), Mar 28 2004
A014107(-n)=a(n), A000384(n+1)=a(n)+1. - Michael Somos Nov 06 2005
G.f.: x*(5-x)/(1-x)^3 - Paul Barry (pbarry(AT)wit.ie), Feb 27 2003
E.g.f: x*(5+2*x)*exp(x). - Michael Somos Nov 06 2005
a(n) = a(n-1)+4*n+1, n>0. [From Vincenzo Librandi, Nov 19 2010]
a(n) = 4*A000217(n)+n. - Bruno Berselli, Feb 11 2011
sum_{n>=1} 1/a(n) = 8/9 -2*log(2)/3 = 0.4267907685155920.. [Jolley eq. 265]
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MAPLE
| A014106 := proc(n) n*(2*n+3) ; end proc: - R. J. Mathar, Feb 13 2011
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MATHEMATICA
| lst={}; Do[AppendTo[lst, n*(2*n+3)], {n, 0, 5!}]; lst s=-1; lst={}; Do[s+=n+1; AppendTo[lst, s], {n, 0, 6!, 4}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
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PROG
| (PARI) a(n)=2*n^2+3*n
(MAGMA) [n*(2*n+3): n in [0..50]]; // Vincenzo Librandi, Apr 25 2011
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CROSSREFS
| Cf. A091823. See A110325 for another version.
Cf. numbers of the form n*(d*n+10-d)/2: A008587, A056000, A028347, A140090, A028895, A045944, A186029, A007742, A022267, A033429, A022268, A049452, A186030, A135703, A152734, A139273.
Sequence in context: A065351 A002503 * A110325 A140342 A055454 A073347
Adjacent sequences: A014103 A014104 A014105 * A014107 A014108 A014109
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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