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Search: id:A055998
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| 0, 3, 7, 12, 18, 25, 33, 42, 52, 63, 75, 88, 102, 117, 133, 150, 168, 187, 207, 228, 250, 273, 297, 322, 348, 375, 403, 432, 462, 493, 525, 558, 592, 627, 663, 700, 738, 777, 817, 858, 900, 943, 987, 1032, 1078, 1125, 1173, 1222, 1272
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OFFSET
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0,2
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COMMENT
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a(n) = A126890(n,2) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 30 2006
If X is an n-set and Y a fixed (n-3)-subset of X then a(n-3) is equal to the number of 2-subsets of X intersecting Y. - Milan R. Janjic (agnus(AT)blic.net), Aug 15 2007
Subsequence of A165157. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Sep 05 2009]
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 193.
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LINKS
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Milan Janjic, Two Enumerative Functions
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FORMULA
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G.f.: x(3-2x)/(1-x)^3.
a(n)=C(n,2)-2*n,n>=5 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006
a(n) = A000217(n) + A005843(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 24 2008]
If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then a(n) = -f(n,n-1,3), for n>=1. [From Milan R. Janjic (agnus(AT)blic.net), Dec 20 2008]
a(n)=n+a(n-1)+1 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 07 2009]
a(n)= A167544(n+8). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 25 2009]
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EXAMPLE
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a(n) = A034856(n+1) - 1 = A000217(n+2) - 3. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Sep 05 2009]
For n=2, a(2)=2+0+1=3; n=3, a(3)=3+3+1=7; n=4, a(4)=4+7+1=12 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 07 2009]
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MAPLE
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a:=n->sum(floor(k+2*n/(k+n)), k=2..n): seq(a(n), n=1..49); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
[seq(binomial(n, 2)-2*n, n=5..53)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006
seq(sum(k-1, k=4..n), n=3..51); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 28 2008
a:=n->sum(numer (k/(k+3)), k=3..n): seq(a(n), n=2..50); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2008
with (combinat):seq((fibonacci(3, n)+n-7)/2, n=2..50); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2008
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MATHEMATICA
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Table[Sum[Binomial[k+1, k], {k, 2, n}], {n, 1, 49}] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 31 2007
...and/or... i=-3; s=3; lst={0}; Do[s+=n+i; If[s>0, AppendTo[lst, s]], {n, 0, 6!, 1}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 30 2008]
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CROSSREFS
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Essentially the same as A027379. Equals A000217(n) - 3. Cf. A000096.
a(n) = A095660(n+1, 2): third column of (1, 3)-Pascal triangle.
Cf. A000096, A001477.
Cf. A002522.
Sequence in context: A095115 A141214 A027379 this_sequence A066379 A024517 A005228
Adjacent sequences: A055995 A055996 A055997 this_sequence A055999 A056000 A056001
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KEYWORD
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easy,nonn,new
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AUTHOR
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Barry E. Williams, Jun 14 2000
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