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Search: id:A037270
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| 0, 1, 10, 45, 136, 325, 666, 1225, 2080, 3321, 5050, 7381, 10440, 14365, 19306, 25425, 32896, 41905, 52650, 65341, 80200, 97461, 117370, 140185, 166176, 195625, 228826, 266085, 307720, 354061, 405450
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Sum of first n^2 integers.
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
Sum of the next n multiples of n. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 01 2002
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
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REFERENCES
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T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.
R. A. Wilson, Cosmic Trigger, epilogue of S.-P. Sirag.
T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 4 (2003), 439-445.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
J. D. Bell, A translation of Leonhard Euler's "De Quadratis Magicis", E795
Th. Gruner, A. Kerber, R. Laue, M. Meringer, Mathematics for Combinatorial Chemistry
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FORMULA
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a(n) = a(n-1) + n^3 + (n-1)^3.
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
a(n) = Sum{k=0..n^2, k} - William A. Tedeschi (fynmun(AT)hotmail.com), Feb 27 2008
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MATHEMATICA
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Table[ n^2*((n^2 + 1)/2), {n, 0, 30} ]
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CROSSREFS
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Sequence in context: A045852 A105938 A022605 this_sequence A027800 A005714 A061772
Adjacent sequences: A037267 A037268 A037269 this_sequence A037271 A037272 A037273
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Aaron Gulliver (gulliver(AT)elec.canterbury.ac.nz)
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EXTENSIONS
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Reference from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 22 1999
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