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A050915 a(n) = n*4^n + 1.

%I A050915 #32 Sep 18 2024 17:53:42
%S A050915 1,5,33,193,1025,5121,24577,114689,524289,2359297,10485761,46137345,
%T A050915 201326593,872415233,3758096385,16106127361,68719476737,292057776129,
%U A050915 1236950581249,5222680231937,21990232555521,92358976733185
%N A050915 a(n) = n*4^n + 1.
%H A050915 Vincenzo Librandi, <a href="/A050915/b050915.txt">Table of n, a(n) for n = 0..1000</a>
%H A050915 Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.htm">Factors of Cullen and Woodall numbers</a>.
%H A050915 Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/gcw.htm">Generalized Cullen and Woodall numbers</a>.
%H A050915 Amelia Carolina Sparavigna, <a href="https://doi.org/10.5281/zenodo.3471358">The groupoids of Mersenne, Fermat, Cullen, Woodall and other Numbers and their representations by means of integer sequences</a>, Politecnico di Torino, Italy (2019), [math.NT].
%H A050915 Amelia Carolina Sparavigna, <a href="https://doi.org/10.18483/ijSci.2188">Some Groupoids and their Representations by Means of Integer Sequences</a>, International Journal of Sciences (2019) Vol. 8, No. 10.
%H A050915 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-24,16).
%F A050915 From _Colin Barker_, Oct 14 2012: (Start)
%F A050915 a(n) = 9*a(n-1) - 24*a(n-2) + 16*a(n-3).
%F A050915 G.f.: -(12*x^2 - 4*x + 1)/((x-1)*(4*x-1)^2). (End)
%F A050915 E.g.f.: exp(x)*(1 + 4*exp(3*x)*x). - _Stefano Spezia_, Jan 05 2020
%t A050915 CoefficientList[Series[-(12 x^2 - 4 x + 1)/((x - 1) (4 x - 1)^2), {x, 0, 21}], x] (* _Michael De Vlieger_, Jan 04 2020 *)
%t A050915 Table[n*4^n+1,{n,0,30}] (* or *) LinearRecurrence[{9,-24,16},{1,5,33},30] (* _Harvey P. Dale_, Sep 18 2024 *)
%o A050915 (Magma) [ n*4^n+1: n in [0..30]]; // _Vincenzo Librandi_, Sep 16 2011
%Y A050915 Cf. A002064.
%K A050915 nonn,easy
%O A050915 0,2
%A A050915 _N. J. A. Sloane_, Dec 30 1999