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A083374
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n^2 * (n^2 - 1)/2
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11
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0, 6, 36, 120, 300, 630, 1176, 2016, 3240, 4950, 7260, 10296, 14196, 19110, 25200, 32640, 41616, 52326, 64980, 79800, 97020, 116886, 139656, 165600, 195000, 228150, 265356, 306936, 353220, 404550, 461280, 523776, 592416, 667590, 749700, 839160
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Triangular numbers t_n as n runs through the squares.
Comment from J. M. Bergot, Jul 14 2011: (Start)
Partial sums of A055112: If one generated Pythagorean primitive triangles from n, n+1, then the collective areas of n of them would be equal to the numbers in this sequence. The sum of the first three triangles is 6+30+84=120 which is the third nonzero term of the sequence. (End)
Second leg of Pythagorean triangles with smallest side a cube: A000578(n)^2 + a(n)^2 = A037270(n)^2. - Martin Renner, Nov 12 2011
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REFERENCES
| Albert H. Beiler, Recreations in the theory of numbers, New York: Dover, (2nd ed.) 1966, p. 106, table 55.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
| a(n) = A047928(n)/2 = A002415(n+1)*6 = A006011(n+1)*2 = A008911(n+1)*3. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
a(n)=binomial(n^2,2),n>=1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 07 2008
a(n)= 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). G.f.: -6*x^2*(1+x)/(x-1)^5. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 10 2009]
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MAPLE
| A083374 := proc(n) n^2*(n^2-1)/2 ; end proc: # R. J. Mathar, Aug 23 2011
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MATHEMATICA
| Table[n^2*(n^2-1)/2, {n, 40}] - T. D. Noe (noe(AT)sspectra.com), Oct 25 2006
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PROG
| (PARI) a(n)=binomial(n^2, 2) \\ Charles R Greathouse IV, Aug 23 2011
(MAGMA) [n^2*(n^2-1)/2: n in [1..40]]; // Vincenzo Librandi, Sep 14 2011
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CROSSREFS
| a(n) = (n + 1) * A006002(n).
Cf. A002415, A006011, A008911, A047928.
A008911 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 27 2008]
Sequence in context: A199243 A172137 A061804 * A061707 A056375 A018214
Adjacent sequences: A083371 A083372 A083373 * A083375 A083376 A083377
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KEYWORD
| easy,nonn
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AUTHOR
| Alan Sutcliffe (alansut(AT)ntlworld.com), Jun 05 2003
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EXTENSIONS
| Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Oct 25 2006
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