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Search: id:A006002
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| A006002 |
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n(n+1)^2/2.
(Formerly M1920)
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+0
20
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| 0, 2, 9, 24, 50, 90, 147, 224, 324, 450, 605, 792, 1014, 1274, 1575, 1920, 2312, 2754, 3249, 3800, 4410, 5082, 5819, 6624, 7500, 8450, 9477, 10584, 11774, 13050, 14415, 15872, 17424, 19074, 20825, 22680
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sum of nontriangular numbers between successive triangular numbers. 1, (2), 3, (4, 5), 6, (7, 8, 9), 10, (11, 12, 13, 14), 15, ... Sum of the terms in brackets. Or sum of n consecutive integers beginning with T(n) +1. T(n) = n(n+1)/2. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 27 2005
Row sums of triangle A159797. [From Omar E. Pol (info(AT)polprimos.com), Jul 24 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
Index entries for two-way infinite sequences
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FORMULA
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a(n) is the largest number which is not the sum of distinct numbers of form kn+1, k >= 0 (David W. Wilson).
G.f.: x(x+2)/(1-x)^4. - Michael Somos, Jan 30 2004
C(2+n, 1)*C(2+n, 2). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 10 2006
(Apparently) this is also the splittance (as defined by Hammer & Simeone, 1977) of the Kneser graphs of the form K(n+3,2). [From Felix Goldberg (felixg(AT)tx.technion.ac.il), Jul 13 2009]
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MAPLE
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a:=n->sum ((j+n)*(n+1)/3, j=0..n): seq(a(n), n=0..35); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 17 2006
seq(sum ((n+1)^2/2, k=1..n), n=0..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 10 2007
seq(binomial(n, 2)*n, n=1..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007
seq(mul(binomial(n, k), k=1..2), n=1..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 13 2007
a:=n->sum(k+sum(k, k=1..n), k=1..n):seq(a(n), n=0...35); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 11 2008
a:=n->(sum((numbcomp(n, 3)), j=2..n)):seq(a(n), n=2..37); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 24 2008]
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MATHEMATICA
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Table[(n^3 -n^2 )/2, {n, 1, 41}] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 21 2007
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PROGRAM
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(PARI) a(n)=n*(n+1)^2/2
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CROSSREFS
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A002411(n)=-a(-1-n).
Cf. A159797, A163274. [From Omar E. Pol (info(AT)polprimos.com), Jul 24 2009]
Sequence in context: A133469 A075714 A101583 this_sequence A023662 A131357 A079997
Adjacent sequences: A005999 A006000 A006001 this_sequence A006003 A006004 A006005
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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