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Search: id:A056000
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| 0, 5, 11, 18, 26, 35, 45, 56, 68, 81, 95, 110, 126, 143, 161, 180, 200, 221, 243, 266, 290, 315, 341, 368, 396, 425, 455, 486, 518, 551, 585, 620, 656, 693, 731, 770, 810, 851, 893, 936, 980, 1025, 1071, 1118, 1166, 1215, 1265, 1316, 1368, 1421, 1475
(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 + 3 * A001477, a(n)=A055999 + A001477 and a(n)=A056115 - A001477 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
a(n) = A126890(n,4) for n>3. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 30 2006
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 193.
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FORMULA
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G.f.(x)=x(5-4x)/(1-x)^3.
a(n)=C(n,2)-4*n,n>=9 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006
Equals A028569/2 - 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-1,5), for n>=1. [From Milan R. Janjic (agnus(AT)blic.net), Dec 20 2008]
a(n)=n+a(n-1)+3 (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+3=5; n=3, a(3)=3+5+3=11; n=4, a(4)=4+11+3=18 [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=4..n): seq(a(n), n=3..53); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
[seq(binomial(n, 2)-4*n, n=9..59)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006
a:=n->sum(n/2, j=10..n): seq(a(n), n=9..51); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 12 2007
seq(sum(k, k=5..n), n=4..54); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008
a:=n->sum(numer (k/(k+3)), k=5..n): seq(a(n), n=4..54); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2008
with(finance):seq(add(cashflows([k, k, 8], 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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lst={}; Do[AppendTo[lst, n*(n+9)/2], {n, 0, 5!}]; lst ...and/or... s=0; lst={s}; Do[s+=n+1; AppendTo[lst, s], {n, 4, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
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CROSSREFS
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Equals A000217(n+4)-10. Cf. A000096, A055998 and A055999.
Column m=2 of (1, 5)-Pascal triangle A096940.
Cf. A000096, A055998, A056000, A001477.
Sequence in context: A166039 A145005 A004083 this_sequence A080566 A094684 A140697
Adjacent sequences: A055997 A055998 A055999 this_sequence A056001 A056002 A056003
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KEYWORD
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easy,nonn,new
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AUTHOR
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Barry E. Williams, Jun 16 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000
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