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A254895
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Indices of octagonal numbers (A000567) that are also centered square numbers (A001844).
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3
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1, 13, 53, 1241, 5161, 121573, 505693, 11912881, 49552721, 1167340733, 4855660933, 114387478921, 475805218681, 11208805593493, 46624055769773, 1098348560683361, 4568681660219041, 107626950141375853, 447684178645696213, 10546342765294150201
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OFFSET
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1,2
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COMMENTS
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Also positive integers x in the solutions to 6*x^2 - 4*y^2 - 4*x + 4*y - 2 = 0, the corresponding values of y being A253673.
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LINKS
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FORMULA
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a(n) = a(n-1)+98*a(n-2)-98*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+12*x^3-58*x^2+12*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).
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EXAMPLE
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13 is in the sequence because the 13th octagonal number is 481, which is also the 16th centered square number.
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PROG
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(PARI) Vec(-x*(x^4+12*x^3-58*x^2+12*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*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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