A064750 a(n) = n*12^n + 1.
1, 13, 289, 5185, 82945, 1244161, 17915905, 250822657, 3439853569, 46438023169, 619173642241, 8173092077569, 106993205379073, 1390911669927937, 17974858503684097, 231105323618795521, 2958148142320582657, 37716388814587428865, 479219999055934390273, 6070119988041835610113
Offset: 0
Links
- Harry J. Smith, Table of n, a(n) for n = 0..150
- Paul Leyland, Factors of Cullen and Woodall numbers.
- Paul Leyland, Generalized Cullen and Woodall numbers.
- Index entries for linear recurrences with constant coefficients, signature (25,-168,144).
Programs
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Magma
[n*12^n + 1: n in [0..30]]; // Vincenzo Librandi, Jun 21 2018
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Mathematica
Table[n*12^n+1,{n,0,20}] (* or *) LinearRecurrence[{25,-168,144},{1,13,289},20] (* Harvey P. Dale, Apr 30 2015 *) CoefficientList[Series[(1 - 12 x + 142 x^2 - 250 x^3 + 1680 x^4 - 1440 x^5) / ((1 - 12 x)^2 (1 - x)), {x, 0, 33}], x] (* Vincenzo Librandi, Jun 21 2018 *) -
PARI
a(n) = { n*12^n + 1 } \\ Harry J. Smith, Sep 24 2009
Formula
a(n) = 25*a(n-1) - 168*a(n-2) + 144*a(n-3), a(0)=1, a(1)=13, a(2)=289. - Harvey P. Dale, Apr 30 2015
G.f.: (1 - 12*x + 142*x^2 - 250*x^3 + 1680*x^4 - 1440*x^5)/((1 - 12*x)^2*(1 - x)). - Vincenzo Librandi, Jun 21 2018
From Elmo R. Oliveira, May 03 2025: (Start)
E.g.f.: exp(x)*(1 + 12*x*exp(11*x)).
a(n) = A064758(n) + 2 for n >= 1. (End)