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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
11
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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
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REFERENCES
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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
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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
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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
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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).
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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njas
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