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A024352
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Numbers which are the difference of two positive squares, c^2 - b^2 with 1 <= b < c.
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17
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3, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 88, 89, 91, 92, 93
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| These are the solutions to the equation x^2 + xy = n where y mod 2 is zero, y is positive and x is any positive integer. - Andrew Plewe (aplewe(AT)sbcglobal.net), Oct 19 2007
Ordered different terms of A120070=3,8,5,15,12,7, in which are two 15's,40's,48's. Complement: A139544. (See A139491). [From Paul Curtz (bpcrtz(AT)free.fr), Sep 01 2009]
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Ron Knott, Pythagorean Triples and Online Calculators
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FORMULA
| Consists of all positive integers except 1, 4 and numbers == 2 mod 4.
a(n)=a(n-3)+4, n>4.
G.f.: (-x^4 - 2*x^3 + 2*x^2 + 2*x + 3)/(x^4 - x^3 - x + 1). - Ralf Stephan (ralf(AT)ark.in-berlin.de), before May 13 2008
From Ant King, Oct 03 2011: (Start)
a(n)=7+2 *floor[(n-3)/3]+floor[(n-2)/3]+floor[(n-1)/3]-floor[pi/(2*n^2)]
a(n)=a(n-1)+a(n-3)-a(n-4) for n>5
(End)
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MATHEMATICA
| Union[ Flatten[ Table[ Select[ Table[b^2 - c^2, {c, b - 1}], # < 100 &], {b, 100}]]] (from Robert G. Wilson v Jun 05 2004)
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CROSSREFS
| Same as A042965 except for initial terms - Michael Somos, Jun 08, 2000.
Different from A020884.
Cf. A009005, A020884.
Sequence in context: A025051 A020884 A183855 * A134407 A183868 A144724
Adjacent sequences: A024349 A024350 A024351 * A024353 A024354 A024355
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 19 2008
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