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A065929
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(x,y) = (a(n),a(n+1)) are the solutions of (t(x)+t(y))/(1+xy)) = t(3) = 6, where t(n) denotes the n-th triangular number t(n) = n(n+1)/2.
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0
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3, 35, 416, 4956, 59055, 703703, 8385380, 99920856, 1190664891, 14188057835, 169066029128, 2014604291700, 24006185471271, 286059621363551, 3408709270891340, 40618451629332528, 484012710281098995
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| J.-P. Ehrmann et al., Problem POLYA002, Integer pairs (x,y) for which (x^2+y^2)/(1+pxy) is an integer.
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FORMULA
| a(n) = 2t(m)a(n-1)-a(n-2)-1, a(0) = m, a(1) = m^3+m^2-1 with m = 3.
G.f.: (4x-3)/((1-12x+x^2)(x-1)).
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MAPLE
| g := (4*x-3)/(1-12*x+x^2)/(x-1): s := series(g, x, 40): for i from 0 to 30 do printf(`%d, `, coeff(s, x, i)) od:
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CROSSREFS
| Sequence in context: A089933 A086043 A006767 * A161495 A179135 A100033
Adjacent sequences: A065926 A065927 A065928 * A065930 A065931 A065932
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KEYWORD
| easy,nonn
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AUTHOR
| Floor van Lamoen (fvlamoen(AT)hotmail.com), Nov 29 2001
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EXTENSIONS
| More terms and Maple code from James A. Sellers (sellersj(AT)math.psu.edu), Feb 11, 2002
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