Search: id:A006002
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%I A006002 M1920
%S A006002 0,2,9,24,50,90,147,224,324,450,605,792,1014,1274,1575,
%T A006002 1920,2312,2754,3249,3800,4410,5082,5819,6624,7500,8450,
%U A006002 9477,10584,11774,13050,14415,15872,17424,19074,20825,22680
%N A006002 n(n+1)^2/2.
%C A006002 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
%C A006002 Row sums of triangle A159797. [From Omar E. Pol (info(AT)polprimos.com), 
               Jul 24 2009]
%D A006002 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006002 S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, 
               Chem. Ber. 30 (1897), 1917-1926.
%H A006002 T. D. Noe, <a href="b006002.txt">Table of n, a(n) for n=0..1000</a>
%H A006002 <a href="Sindx_Tu.html#2wis">Index entries for two-way infinite sequences</
               a>
%F A006002 a(n) is the largest number which is not the sum of distinct numbers of 
               form kn+1, k >= 0 (David W. Wilson).
%F A006002 G.f.: x(x+2)/(1-x)^4. - Michael Somos, Jan 30 2004
%F A006002 C(2+n, 1)*C(2+n, 2). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 10 2006
%F A006002 (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]
%p A006002 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
%p A006002 seq(sum ((n+1)^2/2, k=1..n), n=0..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 10 2007
%p A006002 seq(binomial(n,2)*n, n=1..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 25 2007
%p A006002 seq(mul(binomial(n,k),k=1..2),n=1..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Dec 13 2007
%p A006002 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
%p A006002 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]
%t A006002 Table[(n^3 -n^2 )/2, {n,1, 41}] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 21 2007
%o A006002 (PARI) a(n)=n*(n+1)^2/2
%Y A006002 A002411(n)=-a(-1-n).
%Y A006002 Cf. A159797, A163274. [From Omar E. Pol (info(AT)polprimos.com), Jul 
               24 2009]
%Y A006002 Sequence in context: A133469 A075714 A101583 this_sequence A023662 A131357 
               A079997
%Y A006002 Adjacent sequences: A005999 A006000 A006001 this_sequence A006003 A006004 
               A006005
%K A006002 nonn,easy,nice
%O A006002 0,2
%A A006002 N. J. A. Sloane (njas(AT)research.att.com).

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