Search: id:A027480
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%I A027480
%S A027480 0,3,12,30,60,105,168,252,360,495,660,858,1092,1365,1680,
%T A027480 2040,2448,2907,3420,3990,4620,5313,6072,6900,7800,8775,
%U A027480 9828,10962,12180,13485,14880,16368,17952,19635,21420,23310
%N A027480 n(n+1)(n+2)/2.
%C A027480 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.
%C A027480 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
%C A027480 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
%C A027480 Common sum in an (n+1) X (n+1) magic square with entries (0..n^2-1).
%C A027480 Alternate terms of A057587. - Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), 
               Apr 10 2005
%C A027480 A027480=A007531/2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 
               17 2006
%C A027480 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
%C A027480 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]
%H A027480 T. D. Noe, <a href="b027480.txt">Table of n, a(n) for n=0..1000</a>
%H A027480 S. Gartenhaus, <a href="http://arXiv.org/abs/math.CO/0210275">Odd order 
               pandiagonal latin and magic cubes...</a>.
%H A027480 <a href="Sindx_Do.html#domino">Index entries for sequences related to 
               dominoes</a>
%F A027480 a(n) = a(n-1)+A050534(n) = 3*A000292(n-1) = A050534(n)-A050534(n-1).
%F A027480 n*C(2+n, 2). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 10 
               2006
%F A027480 a(n)=numbperm (n,3)/2, n>=2. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 26 2007
%F A027480 Starting with offset 1 = binomial transform of [3, 9, 9, 3, 0, 0, 0]. 
               - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 25 2007
%F A027480 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]
%p A027480 [seq(3*binomial(n,3),n=2..37)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 24 2006
%p A027480 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
%p A027480 a:=n->sum(binomial(n,2),j=0..n): seq(a(n), n=1..36); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Feb 12 2007
%p A027480 seq(numbperm (n,3)/2, n=2..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 26 2007
%p A027480 with(finance):seq(add(cashflows([n*k,k,k], 0 ),k=0..n),n=0..51); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 30 2008
%p A027480 a:=n->sum(k+sum(k, k=0..n), k=0..n):seq(a(n), n=0...43); [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Aug 24 2008]
%p A027480 > n > ----- > i > ) x > f := n -> / -- > ----- i > i = 1 > print(); n 
               ----- \ i ) x n -> / -- ----- i i = 1 > / 2 \ > expand\(1 - x) f(20)/ 
               > print(); 1 10 3 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 x + --- x - - x + 
               - x + -- x + -- x + -- x + --- x + --- x + --- x 360 2 3 12 30 60 
               105 168 252 1 11 1 12 1 13 1 14 1 15 1 16 1 17 + --- x + --- x + 
               --- x + ---- x + ---- x + ---- x + ---- x 495 660 858 1092 1365 1680 
               2040 1 18 1 19 1 20 9 21 1 22 + ---- x + ---- x + ---- x - --- x 
               + -- x 2448 2907 3420 190 20 [From Miklos Bona (bona(AT)math.ufl.edu), 
               Feb 18 2009]
%t A027480 Table[(m^3 - m)/2, {m, 36}] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 21 2007
%Y A027480 1/beta(n, 3) in A061928.
%Y A027480 Antidiagonal sums of array in A001477.
%Y A027480 Cf. A057587, A006003.
%Y A027480 Sequence in context: A051408 A164013 A057671 this_sequence A135503 A048088 
               A064181
%Y A027480 Adjacent sequences: A027477 A027478 A027479 this_sequence A027481 A027482 
               A027483
%K A027480 nonn,nice,easy
%O A027480 0,2
%A A027480 Olivier Gerard (olivier.gerard(AT)gmail.com) and Ken Knowlton (kcknowlton(AT)aol.com)

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