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A027480
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n(n+1)(n+2)/2.
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25
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0, 3, 12, 30, 60, 105, 168, 252, 360, 495, 660, 858, 1092, 1365, 1680, 2040, 2448, 2907, 3420, 3990, 4620, 5313, 6072, 6900, 7800, 8775, 9828, 10962, 12180, 13485, 14880, 16368, 17952, 19635, 21420, 23310
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Write the integers in groups: 0; 1,2; 3,4,5; 6,7,8,9; ... and add the groups - Asher Auel (asher.auel(AT)reed.edu) Jan 06, 2000. Note that each group begins with a triangular number.
Number of edges of the line graph of the complete graph of order n, L(K_n) - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002
Also the number of the total pips on a set of dominoes of type n. (A "3" domino set would have 0-0, 0-1, 0-2, 0-3, 1-1, 1-2, 1-3, 2-2, 2-3, 3-3). - Gerard Schildberger (GerardS(AT)rrt.net), Jun 26 2003
Common sum in an (n+1) X (n+1) magic square with entries (0..n^2-1).
Alternate terms of A057587. - Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Apr 10 2005
A027480=A007531/2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 17 2006
If Y is a 3-subset of an n-set X then, for n>=5, a(n-5) is the number of 4-subsets of X which have exactly one element in common with Y. Also, if Y is a 3-subset of an n-set X then, for n>=5, a(n-5) is the number of (n-5)-subsets of X which have exactly one element in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 28 2007
These numbers, starting with 3, are the denominators of the power series f(x)=(1-x)^2\ln(1/(1-x)), if the numerators are kept at 1. This sequence of denominators starts at the term x^3/3. [From Miklos Bona (bona(AT)math.ufl.edu), Feb 18 2009]
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
S. Gartenhaus, Odd order pandiagonal latin and magic cubes....
Index entries for sequences related to dominoes
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FORMULA
| a(n) = a(n-1)+A050534(n) = 3*A000292(n-1) = A050534(n)-A050534(n-1).
n*C(2+n, 2). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 10 2006
a(n)=numbperm (n,3)/2, n>=2. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2007
Starting with offset 1 = binomial transform of [3, 9, 9, 3, 0, 0, 0]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 25 2007
G.f.: 3*x/(x-1)^4. a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 07 2009]
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MAPLE
| [seq(3*binomial(n, 3), n=2..37)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 24 2006
a:=n->sum ((j+n)*(n+2)/3, j=0..n): seq(a(n), n=0..35); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 17 2006
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MATHEMATICA
| Table[(m^3 - m)/2, {m, 36}] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 21 2007
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PROG
| (PARI) a(n)=3*binomial(n+2, 3) \\ Charles R Greathouse IV, May 23, 2011
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CROSSREFS
| 1/beta(n, 3) in A061928.
Antidiagonal sums of array in A001477.
Cf. A057587, A006003.
Sequence in context: A051408 A164013 A057671 * A135503 A048088 A064181
Adjacent sequences: A027477 A027478 A027479 * A027481 A027482 A027483
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KEYWORD
| nonn,nice,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com) and Ken Knowlton (kcknowlton(AT)aol.com)
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