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A251625
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Numbers n such that the octagonal number N(n) is the sum of three consecutive octagonal numbers.
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2
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483, 1304163, 3523847043, 9521433405123, 25726909536794403, 69514100046985070883, 187827072600044124730563, 507508680651219178036909443, 1371288267292521619011604583523, 3705220390715712763350177547768803, 10011504124425588594050560722466721283
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OFFSET
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1,1
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COMMENTS
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Also nonnegative integers y in the solutions to 18*x^2-6*y^2+24*x+4*y+18 = 0, the corresponding values of x being A251624.
It seems that the least significant digit of each term is 3.
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..291
Index entries for linear recurrences with constant coefficients, signature (2703,-2703,1).
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FORMULA
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a(n) = 2703*a(n-1)-2703*a(n-2)+a(n-3).
G.f.: -3*x*(x^2-462*x+161) / ((x-1)*(x^2-2702*x+1)).
a(n) = (1 + 2*(sqrt(3)+2)*(1351+780*sqrt(3))^(-n) - 2*(sqrt(3)-2)*(1351+780*sqrt(3))^n) / 3. - Colin Barker, May 30 2017
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EXAMPLE
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483 is in the sequence because N(483) = 698901 = 231296+232965+234640 = N(278)+N(279)+N(280).
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PROG
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(PARI) Vec(-3*x*(x^2-462*x+161)/((x-1)*(x^2-2702*x+1)) + O(x^100))
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CROSSREFS
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Cf. A000567, A251624.
Sequence in context: A281047 A158330 A288082 * A156646 A177434 A202444
Adjacent sequences: A251622 A251623 A251624 * A251626 A251627 A251628
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KEYWORD
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nonn,easy
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AUTHOR
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Colin Barker, Dec 06 2014
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STATUS
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approved
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