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A103772
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Larger of two sides in (a,a,a-1)-integer triangle with integer area.
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3
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1, 17, 241, 3361, 46817, 652081, 9082321, 126500417, 1761923521, 24540428881, 341804080817, 4760716702561, 66308229755041, 923554499868017, 12863454768397201, 179164812257692801, 2495443916839302017
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Corresponding areas are: 0, 120, 25080, 4890480, 949077360, 184120982760, ...
Values (x^2 + y^2)/2, where the pair (x, y) satisfies x^2 - 3y^2 = -2, i.e. a(n)={(A001834(n))^2 + (A001835(n))^2}/2 = {(A001834(n))^2 + A046184(n)}/2. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 13 2006
The heights of these triangles are given in A028230. (A028230(n), A045899(n), A103772(n)) forms a primitive pythagorean triple.
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REFERENCES
| J. B. Cosgrave and K. Dilcher, An Introduction to Gauss Factorials, The American Mathematical Monthly, 118 (Nov. 2011), 812-829.
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FORMULA
| Equals (4*A001570(n+1) - 1)/3, n>0. - Ralf Stephan, May 20 2007
a(n) = (A001353(n))^2+(A001353(n+1))^2 [From Johannes Boot (jgboot(AT)absamail.co.za), Oct 26 2010]
a(n) = A052530(n)*A052530(n+1)+1. - Johannes Boot, May 21 2011
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MATHEMATICA
| a[1] = 1; a[2] = 17; a[3] = 241; a[n_] := a[n] = 15a[n - 1] - 15a[n - 2] + a[n - 3]; Table[ a[n] - 1, {n, 17}] (from Robert G. Wilson v Mar 24 2005)
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CROSSREFS
| Cf. A102341, A103974, A016064, A011945, A028230.
Equals (4*A001570(n-1) - 1)/3, n>0.
Sequence in context: A206354 A125474 A142126 * A196987 A051560 A201302
Adjacent sequences: A103769 A103770 A103771 * A103773 A103774 A103775
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KEYWORD
| nonn
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Feb 23 2005
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 24 2005
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