%I A037270
%S A037270 0,1,10,45,136,325,666,1225,2080,3321,5050,7381,10440,14365,
%T A037270 19306,25425,32896,41905,52650,65341,80200,97461,117370,
%U A037270 140185,166176,195625,228826,266085,307720,354061,405450
%N A037270 n^2*(n^2+1)/2.
%C A037270 Sum of first n^2 integers.
%C A037270 Start from xanthene and attach amino acids according to the reaction 
               scheme that describes the reaction between the active sites. See 
               the hyperlink below on chemistry. - rgwv, Aug 02 2002 - Amarnath 
               Murthy (amarnath_murthy(AT)yahoo.com), Aug 01 2002
%C A037270 Sum of the next n multiples of n. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), 
               Aug 01 2002
%C A037270 The sum of the terms in an n X n spiral. These are also triangular numbers. 
               - William A. Tedeschi (fynmun(AT)hotmail.com), Feb 27 2008
%D A037270 T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, 
               Vol. 1, No. 4, pp. 323-332, 2002.
%D A037270 R. A. Wilson, Cosmic Trigger, epilogue of S.-P. Sirag.
%D A037270 T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 
               4 (2003), 439-445.
%H A037270 T. D. Noe, <a href="b037270.txt">Table of n, a(n) for n=0..1000</a>
%H A037270 J. D. Bell, <a href="http://arXiv.org/abs/math.CO/0408230">A translation 
               of Leonhard Euler's "De Quadratis Magicis", E795</a>
%H A037270 Th. Gruner, A. Kerber, R. Laue, M. Meringer, <a href="ftp://ftp.mathe2.uni-bayreuth.de/
               meringer/pdf/MathCombChemSCCE.pdf">Mathematics for Combinatorial 
               Chemistry</a>
%F A037270 a(n) = a(n-1) + n^3 + (n-1)^3.
%F A037270 a(n) = A000537(n)+A000537(n-1), i.e. square of sum of first n integers 
               plus square of sum of first n-1 integers. - Henry Bottomley (se16(AT)btinternet.com), 
               Oct 15 2001
%F A037270 a(n) = Sum{k=0..n^2, k} - William A. Tedeschi (fynmun(AT)hotmail.com), 
               Feb 27 2008
%p A037270 a:=n->add(n+add(binomial(n,2), j=0..n),j=1..n):seq(a(n), n=0..35); [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 26 2008]
%t A037270 Table[ n^2*((n^2 + 1)/2), {n, 0, 30} ]
%Y A037270 Sequence in context: A045852 A105938 A022605 this_sequence A027800 A005714 
               A143671
%Y A037270 Adjacent sequences: A037267 A037268 A037269 this_sequence A037271 A037272 
               A037273
%K A037270 easy,nonn,nice
%O A037270 0,3
%A A037270 Aaron Gulliver (gulliver(AT)elec.canterbury.ac.nz)
%E A037270 Reference from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), 
               Dec 22 1999