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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
Bisection of A165157. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Sep 05 2009]
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 193.
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LINKS
| Milan Janjic, Two Enumerative Functions
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.: x(3-2x)/(1-x)^3.
a(n) = A027379(n), n>0.
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)= A167544(n+8). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 25 2009]
a(n)=n+a(n-1)+2 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
a(n) = sum((k+2)!/(k+1)!,k=1..n) [From Gary Detlefs (gdetlefs(AT)aol.com), Aug 10 2010]
a(n) = A034856(n+1) - 1 = A000217(n+2) - 3. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Sep 05 2009]
a(n) = A014695(n+2)*A178242(n). - Paul Curtz, Jan 16 2011
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MATHEMATICA
| f[n_]:=n*(n+5)/2; f[Range[0, 100]] (*From Vladimir Joseph Stephan Orlovsky, Feb 10 2011*)
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CROSSREFS
| a(n) = A095660(n+1, 2): third column of (1, 3)-Pascal triangle.
Cf. A000096, A001477.
Cf. A002522.
Sequence in context: A095115 A141214 A027379 * A066379 A024517 A005228
Adjacent sequences: A055995 A055996 A055997 * A055999 A056000 A056001
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, Jun 14 2000
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