Search: id:A011379
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%I A011379
%S A011379 0,2,12,36,80,150,252,392,576,810,1100,1452,1872,2366,2940,3600,4352,
%T A011379 5202,6156,7220,8400,9702,11132,12696,14400,16250,18252,20412,22736,
%U A011379 25230,27900,30752,33792,37026,40460,44100,47952,52022,56316,60840
%N A011379 n^2+n^3.
%C A011379 (1) a(n) = sum of second string of n triangular numbers - sum of first 
               n triangular numbers, or the 2n-th partial sum of triangular numbers 
               (A000217 ) - the n-th partial sum of triangular numbers(A000217 ). 
               The same for natural numbers gives squares. (2) a(n) = (n-th triangular 
               number)*(the n-th even number) = n(n+1)/2 * (2n) - Amarnath Murthy 
               (amarnath_murthy(AT)yahoo.com), Nov 05 2002
%C A011379 Let M(n) be the n X n matrix m(i,j)=1/(i+j+x), let P(n,x)=prod(i=0,n-1,
               i!^2)/det(M(n)). Then P(n,x) is a polynomial with integer coefficients 
               of degree n^2 and a(n) is the coefficient of x^(n^2-1). - Benoit 
               Cloitre (benoit7848c(AT)orange.fr), Jan 15 2003
%C A011379 The sequence allows us to find Y values of the equation: (X-Y)^3-XY=0. 
               Sequence gives Y values. To find X values: a(n)=n*(n+1)^2. (see A045991) 
               - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 09 2006
%C A011379 a(2d-1) is the number of self-avoiding walk of length 3 in the d-dimensional 
               hypercubic lattice. - Michael Somos Sep 06 2006
%C A011379 1/2 + 1/12 + 1/36...=((Pi)^2 - 6)/6. [Jolley] - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Dec 20 2006
%C A011379 1/2 + 1/12 + 1/36 +...= (Pi^2 - 6)/6 [Jolley] - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Dec 22 2006
%C A011379 Number of units of a(n) belongs to a periodic sequence: 0, 2, 2, 6, 0.We 
               conclude that a(n) and a(n+5) have the same number of units. [From 
               Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 05 2009]
%D A011379 L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, pp. 
               50, 64.
%H A011379 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas 
               for Some Functions on Finite Sets</a>
%F A011379 a(n) = Sum[Sum[(i+j), {i, 1, n}], {j, 1, n}] - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Oct 12 2004
%F A011379 a(n)sum(sum(n, j=0..n),k=1..n), n>=0 . - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               May 11 2007
%e A011379 a(3)=3^2+3^3=36.
%p A011379 a:=n->sum(n*numbperm (n,1), j=0..n): seq(a(n), n=0..39); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007
%p A011379 a:=n->sum(sum(n, j=0..n),k=1..n): seq(a(n), n=0..39); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), May 11 2007
%p A011379 a:=n->add(add(add(1, j=1..n),j=2..n),j=2..n):seq(a(n), n=1..21); [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 27 2008]
%p A011379 a:=n->sum ((j*(n+1))+(j*(n-1)),j=0..n): seq(a(n),n=0..39); # [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 18 2009]
%t A011379 a[n_]:=n^2;b[n_]:=n^3;lst={};Do[AppendTo[lst,b[n]+a[n]],{n,0,6!}];lst 
               [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 03 2009]
%Y A011379 Cf. A022549. Twice A002411.
%Y A011379 Cf. A045991.
%Y A011379 Sequence in context: A055707 A055699 A062094 this_sequence A073404 A141208 
               A035597
%Y A011379 Adjacent sequences: A011376 A011377 A011378 this_sequence A011380 A011381 
               A011382
%K A011379 nonn,easy
%O A011379 0,2
%A A011379 Glen Burch; Felice Russo (felice.russo(AT)katamail.com)

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