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

1, 5, 33, 193, 1025, 5121, 24577, 114689, 524289, 2359297, 10485761, 46137345, 201326593, 872415233, 3758096385, 16106127361, 68719476737, 292057776129, 1236950581249, 5222680231937, 21990232555521, 92358976733185

Offset: 0

Author

N. J. A. Sloane, Dec 30 1999

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Paul Leyland, Factors of Cullen and Woodall numbers.
• Paul Leyland, Generalized Cullen and Woodall numbers.
• Amelia Carolina Sparavigna, The groupoids of Mersenne, Fermat, Cullen, Woodall and other Numbers and their representations by means of integer sequences, Politecnico di Torino, Italy (2019), [math.NT].
• Amelia Carolina Sparavigna, Some Groupoids and their Representations by Means of Integer Sequences, International Journal of Sciences (2019) Vol. 8, No. 10.
• Index entries for linear recurrences with constant coefficients, signature (9,-24,16).

Crossrefs

Cf. A002064.

Programs

Magma

[ n*4^n+1: n in [0..30]]; // Vincenzo Librandi, Sep 16 2011

Mathematica

CoefficientList[Series[-(12 x^2 - 4 x + 1)/((x - 1) (4 x - 1)^2), {x, 0, 21}], x] (* Michael De Vlieger, Jan 04 2020 *)
Table[n*4^n+1,{n,0,30}] (* or *) LinearRecurrence[{9,-24,16},{1,5,33},30] (* Harvey P. Dale, Sep 18 2024 *)

Formula

From Colin Barker, Oct 14 2012: (Start)

a(n) = 9*a(n-1) - 24*a(n-2) + 16*a(n-3).

G.f.: -(12*x^2 - 4*x + 1)/((x-1)*(4*x-1)^2). (End)

E.g.f.: exp(x)*(1 + 4*exp(3*x)*x). - Stefano Spezia, Jan 05 2020