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A251864
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Numbers n such that the sum of the pentagonal numbers P(n), P(n+1) and P(n+2) is equal to the sum of the octagonal numbers N(m), N(m+1) and N(m+2) for some m.
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2
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3, 208, 4387, 240992, 5063555, 278105520, 5843339043, 320933530048, 6743208193027, 370357015570832, 7781656411415075, 427391675035211040, 8980024755564804483, 493209622633617970288, 10362940786265372959267, 569163477127520102502272
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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^2-9*y^2+24*x-15*y+6 = 0, the corresponding values of x being A251863.
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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*(35*x^3+717*x^2+205*x+3) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).
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EXAMPLE
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3 is in the sequence because P(3)+P(4)+P(5) = 12+22+35 = 69 = 8+21+40 = N(2)+N(3)+N(4).
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MATHEMATICA
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LinearRecurrence[{1, 1154, -1154, -1, 1}, {3, 208, 4387, 240992, 5063555}, 20] (* Harvey P. Dale, Apr 29 2019 *)
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PROG
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(PARI) Vec(-x*(35*x^3+717*x^2+205*x+3)/((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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