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A251896
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Numbers n such that the octagonal number N(n) is equal to the sum of the octagonal numbers N(m) and N(m+1) for some m.
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2
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1, 43, 521, 49235, 600849, 56816763, 693378841, 65566494883, 800158581281, 75663678277835, 923382309419049, 87315819166126323, 1065582384911000881, 100762379654031498523, 1229681148804985597241, 116279698804933183168835, 1419050980138568468214849
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OFFSET
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1,2
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COMMENTS
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Also nonnegative integers y in the solutions to 12*x^2-6*y^2+4*x+4*y+2 = 0, the corresponding values of x being A251895.
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LINKS
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FORMULA
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a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(3*x^4+246*x^3-676*x^2+42*x+1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).
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EXAMPLE
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43 is in the sequence because N(43) = 5461 = 2640+2821 = N(30)+N(31).
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PROG
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(PARI) Vec(-x*(3*x^4+246*x^3-676*x^2+42*x+1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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