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A057769
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a(n) = 4*n^4+8*n^3-4*n-1 = (2*n^2-1)*(2*n^2+4*n+1).
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5
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-1, 7, 119, 527, 1519, 3479, 6887, 12319, 20447, 32039, 47959, 69167, 96719, 131767, 175559, 229439, 294847, 373319, 466487, 576079, 703919, 851927, 1022119, 1216607, 1437599, 1687399, 1968407, 2283119, 2634127, 3024119, 3455879, 3932287, 4456319, 5031047, 5659639, 6345359, 7091567
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| It may be seen that the terms of the (signed) sequence consist of a subset of the odd squares minus two.
One leg of pythagorean triangles with hypotenuse a square: a(n)^2 + A069074(n-1)^2 = A007204(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 53.
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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 0..1000
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FORMULA
| a(0)=-1, a(1)=7, a(2)=119, a(3)=527, a(4)=1519, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5) [From Harvey P. Dale, Oct 20 2011]
G.f.: (x*(x*((x-12)*x-74)-12)+1)/(x-1)^5 [From Harvey P. Dale, Oct 20 2011]
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MATHEMATICA
| Table[4n^4+8n^3-4n-1, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {-1, 7, 119, 527, 1519}, 40] (* From Harvey P. Dale, Oct 20 2011 *)
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CROSSREFS
| a(n) = 4*b(n)^2 - 4*b(n) - 1 where b(n) = n-th pronic number A002378(n).
Sequence in context: A097202 A163202 A076283 * A113667 A192565 A171209
Adjacent sequences: A057766 A057767 A057768 * A057770 A057771 A057772
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KEYWORD
| easy,sign
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AUTHOR
| STUART M. ELLERSTEIN (ellerstein(AT)aol.com), Nov 01 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Nov 02 2000
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