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A254710
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Indices of centered square numbers (A001844) which are also pentagonal numbers (A000326).
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3
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1, 2, 9, 22, 119, 300, 1651, 4172, 22989, 58102, 320189, 809250, 4459651, 11271392, 62114919, 156990232, 865149209, 2186591850, 12049974001, 30455295662, 167834486799, 424187547412, 2337632841179, 5908170368100, 32559025289701, 82290197605982
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OFFSET
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1,2
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COMMENTS
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Also positive integers y in the solutions to 3*x^2 - 4*y^2 - x + 4*y - 2 = 0, the corresponding values of x being A254709.
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LINKS
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FORMULA
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a(n) = a(n-1)+14*a(n-2)-14*a(n-3)-a(n-4)+a(n-5).
G.f.: x*(x^3+7*x^2-x-1) / ((x-1)*(x^2-4*x+1)*(x^2+4*x+1)).
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EXAMPLE
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9 is in the sequence because the 9th centered square number is 145, which is also the 10th pentagonal number.
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PROG
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(PARI) Vec(x*(x^3+7*x^2-x-1)/((x-1)*(x^2-4*x+1)*(x^2+4*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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