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Search: id:A101859
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| A101859 |
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a(n) = 11 + (23*n)/2 + n^2/2. |
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+0
3
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| 0, 11, 23, 36, 50, 65, 81, 98, 116, 135, 155, 176, 198, 221, 245, 270, 296, 323, 351, 380, 410, 441, 473, 506, 540, 575, 611, 648, 686, 725, 765, 806, 848, 891, 935, 980, 1026, 1073, 1121, 1170, 1220, 1271, 1323, 1376, 1430, 1485, 1541, 1598, 1656, 1715, 1775, 1836
(list; graph; listen)
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OFFSET
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-1,2
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COMMENT
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a(n)=A000096 + 9 * A001477 and a(n)=A056126 + A001477. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
a(n) = A126890(n+1,10) for n>8. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 30 2006
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LINKS
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C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.
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FORMULA
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a(n)=C(n,2)-10*n,n>=21 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 26 2006
G.f.: (11-10x)/(1-x)^3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 09 2008]
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-1) = -f(n,n-1,11), for n>=1. [From Milan R. Janjic (agnus(AT)blic.net), Dec 20 2008]
a(n)=n+a(n-1)+9 (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+9=11; n=3, a(3)=3+11+9=23; n=4, a(4)=4+23+9=36 [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=10..n): seq(a(n), n=10..57); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
[seq(binomial(n, 2)-10*n, n=21..72)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 26 2006
a:=n->sum(numer (k/(k+3)), k=11..n): seq(a(n), n=10..61); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2008
with(finance):seq(add(cashflows([2, k, 8], 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=-10; 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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Cf. A000096, A056126, A001477.
Sequence in context: A136771 A017653 A139793 this_sequence A079664 A160268 A135978
Adjacent sequences: A101856 A101857 A101858 this_sequence A101860 A101861 A101862
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KEYWORD
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easy,nonn
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AUTHOR
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Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 07 2006
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