%I A055999
%S A055999 0,4,9,15,22,30,39,49,60,72,85,99,114,130,147,165,184,204,225,247,270,
%T A055999 294,319,345,372,400,429,459,490,522,555,589,624,660,697,735,774,814,
%U A055999 855,897,940,984,1029,1075,1122,1170,1219,1269,1320,1372,1425,1479
%N A055999 a(n)=n*(n+7)/2.
%C A055999 a(n) = A126890(n,3) for n>2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Dec 30 2006
%C A055999 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
%D A055999 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, 
               p. 193.
%H A055999 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%F A055999 G.f.(x)=x(4-3x)/(1-x)^3.
%F A055999 a(n)=C(n,2)-3*n,n>=7 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 25 2006
%F A055999 Equals A028563/2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 
               12 2007
%F A055999 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]
%F A055999 a(n)=n+a(n-1)+2 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 18 2009]
%e A055999 For n=2, a(2)=2+0+2=4; n=3, a(3)=3+4+2=9; a(4)=4+9+2=15 [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Nov 18 2009]
%p A055999 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
%p A055999 [seq(binomial(n,2)-3*n,n=7..58)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 25 2006
%p A055999 a:=n->sum(n/2,j=8..n): seq(a(n), n=7..58); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Feb 12 2007
%p A055999 seq(sum(k-1, k=5..n), n=4..55); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 28 2008
%p A055999 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
%p A055999 with (combinat):seq((fibonacci(3, n)+n-13)/2, n=3..54); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 07 2008
%t A055999 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]
%Y A055999 Equals A000217(n+3)-6. Cf. A000096, A055998, A074171.
%Y A055999 Third column (m=2) of (1, 4)-Pascal triangle A095666.
%Y A055999 Cf. A000096, A055998, A056000, A001477.
%Y A055999 Cf. A002522.
%Y A055999 Sequence in context: A073046 A066495 A134227 this_sequence A022945 A022443 
               A079423
%Y A055999 Adjacent sequences: A055996 A055997 A055998 this_sequence A056000 A056001 
               A056002
%K A055999 easy,nonn,new
%O A055999 0,2
%A A055999 Barry E. Williams, Jun 16 2000
%E A055999 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000