%I A056115
%S A056115 0,6,13,21,30,40,51,63,76,90,105,121,138,156,175,195,216,238,261,285,
%T A056115 310,336,363,391,420,450,481,513,546,580,615,651,688,726,765,805,846,
%U A056115 888,931,975,1020,1066,1113,1161,1210,1260,1311,1363,1416,1470,1525
%N A056115 a(n)=n*(n+11)/2.
%C A056115 a(n)=A000096 + 4 * A001477, a(n)=A056000 + A001477 and a(n)=A056119 - 
               A001477 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
%C A056115 a(n) = A126890(n,5) for n>4. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Dec 30 2006
%D A056115 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, 
               pps. 194-196.
%F A056115 G.f.(x)=x(6-5x)/(1-x)^3.
%F A056115 a(n)=C(n,2)-5*n,n>=11 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 25 2006
%F A056115 Equals A119412/2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 
               12 2007
%F A056115 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-1,6), for n>=1. [From Milan 
               R. Janjic (agnus(AT)blic.net), Dec 20 2008]
%F A056115 a(n)=n+a(n-1)+4 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 19 2009]
%e A056115 For n=2, a(2)=2+0+4=6; n=3, a(3)=3+6+4=13; n=4, a(4)=4+13+4=21 [From 
               Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 19 2009]
%p A056115 a:=n->sum(floor(k+2*n/(k+n)), k=5..n): seq(a(n),n=4..53); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
%p A056115 [seq(binomial(n,2)-5*n,n=11..61)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 25 2006
%p A056115 a:=n->sum(n/2,j=12..n): seq(a(n), n=11..61); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Feb 12 2007
%p A056115 seq((GAMMA(n+7)/GAMMA(n+5)-30)/2,n=0..50); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 23 2007
%p A056115 seq(sum(k, k=6..n), n=5..55); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Feb 22 2008
%p A056115 a:=n->sum(numer (k/(k+3)), k=6..n): seq(a(n), n=5..55); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), May 31 2008
%p A056115 with(finance):seq(add(cashflows([k, k, 10], 0 ), k=1..n)/2, n=0..45);
               # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
%t A056115 s=0;lst={s};Do[s+=n+1;AppendTo[lst, s], {n, 5, 5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
%Y A056115 Cf. A055999 and A056000.
%Y A056115 Third column of Pascal (1, 6) triangle A096956.
%Y A056115 Cf. A000096, A056119, A056000, A001477.
%Y A056115 Sequence in context: A004919 A017053 A046040 this_sequence A101247 A072212 
               A028872
%Y A056115 Adjacent sequences: A056112 A056113 A056114 this_sequence A056116 A056117 
               A056118
%K A056115 easy,nonn,new
%O A056115 0,2
%A A056115 Barry E. Williams, Jul 04 2000
%E A056115 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000