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<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
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(PARI) a(n) = 3*n^2 + n + 3; \\ Michel Marcus, Dec 15 2017
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LinearRecurrence[{3, -3, 1}, {3, 7, 17}, 52] (* or *)
CoefficientList[Series[-(5 x^2 - 2 x + 3)/(x - 1)^3, {x, 0, 51}], x] (* Robert G. Wilson v, Nov 29 2017 *)
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Numbers represented as the palindrome 313 in number base n including base n=1, base 2 (binary) and base 3 with 'illegal' digit 3: 313(_1)=7, 313(_2)=17, 313(_3)=33, ... 313(_9)=255, 313(_10)=313, ...
313 in base 7 is 3*7^2 + 1*7 + 3 = 157.
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