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A056115
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a(n)=n*(n+11)/2.
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10
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0, 6, 13, 21, 30, 40, 51, 63, 76, 90, 105, 121, 138, 156, 175, 195, 216, 238, 261, 285, 310, 336, 363, 391, 420, 450, 481, 513, 546, 580, 615, 651, 688, 726, 765, 805, 846, 888, 931, 975, 1020, 1066, 1113, 1161, 1210, 1260, 1311, 1363, 1416, 1470, 1525
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)=A000096 + 4 * A001477, a(n)=A056000 + A001477 and a(n)=A056119 - A001477 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
a(n) = A126890(n,5) for n>4. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 30 2006
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 194-196.
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FORMULA
| G.f.(x)=x(6-5x)/(1-x)^3.
a(n)=C(n,2)-5*n,n>=11 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006
Equals A119412/2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 12 2007
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-1,6), for n>=1. [From Milan R. Janjic (agnus(AT)blic.net), Dec 20 2008]
a(n)=n+a(n-1)+5 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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EXAMPLE
| a(1)=1+0+5=6; a(2)=2+6+5=13; a(3)=3+13+5=21 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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MAPLE
| a:=n->sum(floor(k+2*n/(k+n)), k=5..n): seq(a(n), n=4..53); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
[seq(binomial(n, 2)-5*n, n=11..61)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006
a:=n->sum(n/2, j=12..n): seq(a(n), n=11..61); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 12 2007
seq((GAMMA(n+7)/GAMMA(n+5)-30)/2, n=0..50); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2007
seq(sum(k, k=6..n), n=5..55); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008
a:=n->sum(numer (k/(k+3)), k=6..n): seq(a(n), n=5..55); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2008
with(finance):seq(add(cashflows([k, k, 10], 0 ), k=1..n)/2, n=0..45); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
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MATHEMATICA
| s=0; lst={s}; Do[s+=n+1; AppendTo[lst, s], {n, 5, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
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CROSSREFS
| Cf. A055999 and A056000.
Third column of Pascal (1, 6) triangle A096956.
Cf. A000096, A056119, A056000, A001477.
Sequence in context: A172330 A017053 A046040 * A173358 A101247 A072212
Adjacent sequences: A056112 A056113 A056114 * A056116 A056117 A056118
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, Jul 04 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000
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