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Search: id:A051942
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| A051942 |
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Truncated triangular numbers: a(n)=n*(n+1)/2-3*t*(t+1)/2, t=5. |
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+0
4
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| 0, 10, 21, 33, 46, 60, 75, 91, 108, 126, 145, 165, 186, 208, 231, 255, 280, 306, 333, 361, 390, 420, 451, 483, 516, 550, 585, 621, 658, 696, 735, 775, 816, 858, 901, 945, 990, 1036, 1083, 1131, 1180, 1230, 1281, 1333, 1386, 1440, 1495, 1551, 1608, 1666
(list; graph; listen)
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OFFSET
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9,2
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COMMENT
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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
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FORMULA
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With offset 0, a(n)=n*(n+19)/2. G.f.(x)=x(10-9x)/(1-x)^3 - Barry E. Williams, Jul 09 2000
a(n)=C(n,2)-9*n,n>=19 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 26 2006
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]
a(n)=n+a(n-1)+8 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 19 2009]
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EXAMPLE
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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]
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MAPLE
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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
[seq(binomial(n, 2)-9*n, n=19..68)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 26 2006
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
with(finance):seq(add(cashflows([2, k, 7], 0 ), k=1..n), n=0..50); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2008
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MATHEMATICA
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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]
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CROSSREFS
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a(n)=A000217(n)-45, n>8
Cf. A000096, A056121, A079664, A001477.
Sequence in context: A065438 A017509 A072806 this_sequence A082581 A075846 A164714
Adjacent sequences: A051939 A051940 A051941 this_sequence A051943 A051944 A051945
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 21 1999
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EXTENSIONS
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More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
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