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Search: id:A014106
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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; listen)
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OFFSET
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0,2
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COMMENT
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This sequence minus 1 (i.e. a(n) = 2*n^2 + 3*n - 1) is sequence A091823. - Howard A. Landman (howard(AT)riverrock.org), Mar 28 2004
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
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LINKS
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Milan Janjic, Two Enumerative Functions
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FORMULA
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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+2x)exp(x). - Michael Somos Nov 06 2005
a(n)=4*n+a(n-1)-3 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
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EXAMPLE
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For n=2, a(2)=4*2+0-3=5; n=3, a(3)=4*3+5-3=14; n=4, a(4)=4*4+14-3=27 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
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MAPLE
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with(finance):seq(add(cashflows([n, k, k], 0 ), k=1..n-2), n=2..51); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 30 2008
a:=n->sum(1+sum(2, k=0..n), k=1..n):seq(a(n), n=0...43); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 24 2008]
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MATHEMATICA
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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]
Table[Sum[(2*i + n - 1), {i, 2, n}], {n, 1, 47}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]
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PROGRAM
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(PARI) a(n)=n*(2*n+3)
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CROSSREFS
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Cf. A091823. See A110325 for another version.
Sequence in context: A071421 A065351 A002503 this_sequence A110325 A140342 A055454
Adjacent sequences: A014103 A014104 A014105 this_sequence A014107 A014108 A014109
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KEYWORD
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nonn,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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