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A055999
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a(n)=n*(n+7)/2.
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17
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0, 4, 9, 15, 22, 30, 39, 49, 60, 72, 85, 99, 114, 130, 147, 165, 184, 204, 225, 247, 270, 294, 319, 345, 372, 400, 429, 459, 490, 522, 555, 589, 624, 660, 697, 735, 774, 814, 855, 897, 940, 984, 1029, 1075, 1122, 1170, 1219, 1269, 1320, 1372, 1425, 1479
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) = A126890(n,3) for n>2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 30 2006
If X is an n-set and Y a fixed (n-4)-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
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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 entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.(x)=x(4-3x)/(1-x)^3.
a(n)=C(n,2)-3*n,n>=7 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006
Equals A028563/2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 12 2007
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-1,4), for n>=1. [From Milan R. Janjic (agnus(AT)blic.net), Dec 20 2008]
a(n)=n+a(n-1)+3 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
a(n) = sum((k+3)!/(k+2)!,k=1..n) [From Gary Detlefs (gdetlefs(AT)aol.com), Aug 10 2010]
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MAPLE
| a:=n->sum(floor(k+2*n/(k+n)), k=3..n): seq(a(n), n=2..53); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
[seq(binomial(n, 2)-3*n, n=7..58)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006
a:=n->sum(n/2, j=8..n): seq(a(n), n=7..58); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 12 2007
seq(sum(k-1, k=5..n), n=4..55); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 28 2008
a:=n->sum(numer (k/(k+3)), k=4..n): seq(a(n), n=3..54); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2008
with (combinat):seq((fibonacci(3, n)+n-13)/2, n=3..54); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2008
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MATHEMATICA
| lst={}; Do[AppendTo[lst, n*(n+7)/2], {n, 0, 5!}]; lst ...and/or... s=0; lst={s}; Do[s+=n+1; AppendTo[lst, s], {n, 3, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
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CROSSREFS
| Equals A000217(n+3)-6. Cf. A000096, A055998, A074171.
Third column (m=2) of (1, 4)-Pascal triangle A095666.
Cf. A000096, A055998, A056000, A001477, A002522.
Sequence in context: A073046 A066495 A134227 * A022945 A022443 A079423
Adjacent sequences: A055996 A055997 A055998 * A056000 A056001 A056002
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, Jun 16 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000
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