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Search: id:A028347
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| 0, 5, 12, 21, 32, 45, 60, 77, 96, 117, 140, 165, 192, 221, 252, 285, 320, 357, 396, 437, 480, 525, 572, 621, 672, 725, 780, 837, 896, 957, 1020, 1085, 1152, 1221, 1292, 1365, 1440, 1517, 1596, 1677, 1760, 1845
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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Sequence allows us to find X values of the equation: X^3 + 4*X^2 = Y^2. To find Y values: b(n)=n*(n^2 - 4). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 06 2007
Discriminants of binary forms x^2 + n*x*y + y^2 (for n>1) - Artur Jasinski (grafix(AT)csl.pl), Apr 28 2008
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REFERENCES
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A. Connes, Noncommutative Geometry, Academic Press, 1994, p. 35.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Eric Weisstein's World of Mathematics, Near-Square Prime
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FORMULA
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Except for initial term, denominators of wavelengths of hydrogen lines.
a(n)=n(n+4). G.f.(x)=x(5-3x)/(1-x)^3 - Barry E. Williams, Jun 16 2000
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MAPLE
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a:=n->sum(n, j=5..n): seq(a(n), n=4..45); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 12 2007
with(combinat):seq(fibonacci(3, i)-5, i=2..43); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008
with(finance):seq(add(cashflows([k, k, 3], 0 ), k=1..n), n=0..45); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
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MATHEMATICA
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lst={}; Do[AppendTo[lst, n^2-4], {n, 2, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 06 2008]
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PROGRAM
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(Other) SAGE: [lucas_number2(2, n, 2) for n in xrange(2, 44)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 12 2009]
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CROSSREFS
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a(n), n>=3, second column (used for the Balmer series of the hydrogen atom) of triangle A120070.
Cf. A005563, A046092, A001082, A002378, A036666, A062717.
Adjacent sequences: A028344 A028345 A028346 this_sequence A028348 A028349 A028350
Sequence in context: A063559 A121291 A097984 this_sequence A038794 A131976 A074376
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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