%I A055998
%S A055998 0,3,7,12,18,25,33,42,52,63,75,88,102,117,133,150,168,187,207,228,250,
%T A055998 273,297,322,348,375,403,432,462,493,525,558,592,627,663,700,738,777,
%U A055998 817,858,900,943,987,1032,1078,1125,1173,1222,1272
%N A055998 n*(n+5)/2.
%C A055998 a(n) = A126890(n,2) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Dec 30 2006
%C A055998 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
%C A055998 Subsequence of A165157. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), 
               Sep 05 2009]
%D A055998 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, 
               p. 193.
%H A055998 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%F A055998 G.f.: x(3-2x)/(1-x)^3.
%F A055998 a(n)=C(n,2)-2*n,n>=5 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 25 2006
%F A055998 a(n) = A000217(n) + A005843(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Sep 24 2008]
%F A055998 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]
%F A055998 a(n)=n+a(n-1)+1 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 07 2009]
%F A055998 a(n)= A167544(n+8). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 25 2009]
%e A055998 a(n) = A034856(n+1) - 1 = A000217(n+2) - 3. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), 
               Sep 05 2009]
%e A055998 For n=2, a(2)=2+0+1=3; n=3, a(3)=3+3+1=7; n=4, a(4)=4+7+1=12 [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Nov 07 2009]
%p A055998 a:=n->sum(floor(k+2*n/(k+n)), k=2..n): seq(a(n),n=1..49); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
%p A055998 [seq(binomial(n,2)-2*n,n=5..53)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 25 2006
%p A055998 seq(sum(k-1, k=4..n), n=3..51); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 28 2008
%p A055998 a:=n->sum(numer (k/(k+3)), k=3..n): seq(a(n), n=2..50); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), May 31 2008
%p A055998 with (combinat):seq((fibonacci(3, n)+n-7)/2, n=2..50); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 07 2008
%t A055998 Table[Sum[Binomial[k+1, k], {k, 2, n}], {n, 1, 49}] - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Mar 31 2007
%t A055998 ...and/or... i=-3;s=3;lst={0};Do[s+=n+i;If[s>0, AppendTo[lst, s]], {n, 
               0, 6!, 1}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Oct 30 2008]
%Y A055998 Essentially the same as A027379. Equals A000217(n) - 3. Cf. A000096.
%Y A055998 a(n) = A095660(n+1, 2): third column of (1, 3)-Pascal triangle.
%Y A055998 Cf. A000096, A001477.
%Y A055998 Cf. A002522.
%Y A055998 Sequence in context: A095115 A141214 A027379 this_sequence A066379 A024517 
               A005228
%Y A055998 Adjacent sequences: A055995 A055996 A055997 this_sequence A055999 A056000 
               A056001
%K A055998 easy,nonn,new
%O A055998 0,2
%A A055998 Barry E. Williams, Jun 14 2000