Search: id:A051942
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%I A051942
%S A051942 0,10,21,33,46,60,75,91,108,126,145,165,186,208,231,255,280,306,333,
%T A051942 361,390,420,451,483,516,550,585,621,658,696,735,775,816,858,901,945,
%U A051942 990,1036,1083,1131,1180,1230,1281,1333,1386,1440,1495,1551,1608,1666
%N A051942 Truncated triangular numbers: a(n)=n*(n+1)/2-3*t*(t+1)/2, t=5.
%C A051942 a(n)=A000096 + 8 * A001477, a(n)=A056126 + A001477, a(n)=A079664 - A001477 
               if (A079664(0)=0) - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Oct 01 2006
%F A051942 With offset 0, a(n)=n*(n+19)/2. G.f.(x)=x(10-9x)/(1-x)^3 - Barry E. Williams, 
               Jul 09 2000
%F A051942 a(n)=C(n,2)-9*n,n>=19 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 26 2006
%F A051942 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+9) = -f(n,n-1,10), for n>=1. [From 
               Milan R. Janjic (agnus(AT)blic.net), Dec 20 2008]
%F A051942 a(n)=n+a(n-1)+8 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 19 2009]
%e A051942 For n=2, a(2)=2+0+8=10; n=3, a(3)=3+10+8=21; n=4, a(4)=4+21+8=33 [From 
               Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 19 2009]
%p A051942 a:=n->sum(floor(k+2*n/(k+n)), k=9..n): seq(a(n),n=8..57); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
%p A051942 [seq(binomial(n,2)-9*n,n=19..68)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 26 2006
%p A051942 a:=n->sum(numer (k/(k+3)), k=10..n): seq(a(n), n=9..58); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), May 31 2008
%p A051942 with(finance):seq(add(cashflows([2,k,7], 0 ),k=1..n),n=0..50); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2008
%t A051942 i=-9;s=0;lst={};Do[s+=n+i;If[s>=0, AppendTo[lst, s]], {n, 0, 6!, 1}];
               lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 29 2008]
%Y A051942 a(n)=A000217(n)-45, n>8
%Y A051942 Cf. A000096, A056121, A079664, A001477.
%Y A051942 Sequence in context: A065438 A017509 A072806 this_sequence A082581 A075846 
               A164714
%Y A051942 Adjacent sequences: A051939 A051940 A051941 this_sequence A051943 A051944 
               A051945
%K A051942 easy,nice,nonn,new
%O A051942 9,2
%A A051942 Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 21 1999
%E A051942 More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 
               2006

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