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Search: id:A056119
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| 0, 7, 15, 24, 34, 45, 57, 70, 84, 99, 115, 132, 150, 169, 189, 210, 232, 255, 279, 304, 330, 357, 385, 414, 444, 475, 507, 540, 574, 609, 645, 682, 720, 759, 799, 840, 882, 925, 969, 1014, 1060, 1107, 1155, 1204, 1254, 1305, 1357, 1410, 1464, 1519, 1575
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)=A000096 + 5 * A001477, a(n)=A056115 + A001477 and a(n)=A056121 - A001477 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
a(n) = A126890(n,6) for n>5. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 30 2006
a(n)=A000096(n) + 5 * A001477(n), a(n)=A056115(n) + A001477(n), a(n)=A056121(n) - A001477(n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008
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REFERENCES
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P. Lafer, Discovering the square-triangular numbers, Fib. Quart. 9 (1971), pps. 93-105.
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FORMULA
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G.f.(x)=x(7-6x)/(1-x)^3.
a(n)=C(n,2)-6*n,n>=13 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 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) = -f(n,n-1,7), for n>=1. [From Milan R. Janjic (agnus(AT)blic.net), Dec 20 2008]
a(n)=n+a(n-1)+5 (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+5=7; n=3, a(3)=3+7+5=15; n=4, a(4)=4+15+5=24 [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=6..n): seq(a(n), n=5..55); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
[seq(binomial(n, 2)-6*n, n=13..63)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006
seq(sum(k, k=7..n), n=6..56); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008
a:=n->sum(numer (k/(k+3)), k=7..n): seq(a(n), n=6..56); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2008
with(finance):seq(add(cashflows([k, k, 12], 0 ), k=1..n)/2, n=0..45); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
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MATHEMATICA
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i=-6; 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. A056115.
Cf. A000096, A056115, A056121, A056000, A001477.
Cf. A000096, A056115, A056121.
Sequence in context: A056828 A113505 A076796 this_sequence A082111 A154935 A012480
Adjacent sequences: A056116 A056117 A056118 this_sequence A056120 A056121 A056122
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KEYWORD
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easy,nonn,new
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AUTHOR
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Barry E. Williams, Jul 04 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 05 2000
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