%I A056000
%S A056000 0,5,11,18,26,35,45,56,68,81,95,110,126,143,161,180,200,221,243,266,
%T A056000 290,315,341,368,396,425,455,486,518,551,585,620,656,693,731,770,810,
%U A056000 851,893,936,980,1025,1071,1118,1166,1215,1265,1316,1368,1421,1475
%N A056000 a(n)=n*(n+9)/2.
%C A056000 a(n)=A000096 + 3 * A001477, a(n)=A055999 + A001477 and a(n)=A056115 - 
               A001477 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
%C A056000 a(n) = A126890(n,4) for n>3. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Dec 30 2006
%D A056000 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, 
               p. 193.
%F A056000 G.f.(x)=x(5-4x)/(1-x)^3.
%F A056000 a(n)=C(n,2)-4*n,n>=9 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 25 2006
%F A056000 Equals A028569/2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 
               12 2007
%F A056000 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-1,5), for n>=1. [From Milan 
               R. Janjic (agnus(AT)blic.net), Dec 20 2008]
%F A056000 a(n)=n+a(n-1)+3 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 19 2009]
%e A056000 For n=2, a(2)=2+0+3=5; n=3, a(3)=3+5+3=11; n=4, a(4)=4+11+3=18 [From 
               Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 19 2009]
%p A056000 a:=n->sum(floor(k+2*n/(k+n)), k=4..n): seq(a(n),n=3..53); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
%p A056000 [seq(binomial(n,2)-4*n,n=9..59)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 25 2006
%p A056000 a:=n->sum(n/2,j=10..n): seq(a(n), n=9..51); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Feb 12 2007
%p A056000 seq(sum(k, k=5..n), n=4..54); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Feb 22 2008
%p A056000 a:=n->sum(numer (k/(k+3)), k=5..n): seq(a(n), n=4..54); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), May 31 2008
%p A056000 with(finance):seq(add(cashflows([k, k, 8], 0 ), k=1..n)/2, n=0..45); 
               # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
%t A056000 lst={};Do[AppendTo[lst, n*(n+9)/2], {n, 0, 5!}];lst ...and/or... s=0;
               lst={s};Do[s+=n+1;AppendTo[lst, s], {n, 4, 5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
%Y A056000 Equals A000217(n+4)-10. Cf. A000096, A055998 and A055999.
%Y A056000 Column m=2 of (1, 5)-Pascal triangle A096940.
%Y A056000 Cf. A000096, A055998, A056000, A001477.
%Y A056000 Sequence in context: A166039 A145005 A004083 this_sequence A080566 A094684 
               A140697
%Y A056000 Adjacent sequences: A055997 A055998 A055999 this_sequence A056001 A056002 
               A056003
%K A056000 easy,nonn,new
%O A056000 0,2
%A A056000 Barry E. Williams, Jun 16 2000
%E A056000 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000