A060416 a(n) = n*4^n - 1, with a(0) = 1.
1, 3, 31, 191, 1023, 5119, 24575, 114687, 524287, 2359295, 10485759, 46137343, 201326591, 872415231, 3758096383, 16106127359, 68719476735, 292057776127, 1236950581247, 5222680231935, 21990232555519, 92358976733183, 387028092977151, 1618481116086271, 6755399441055743
Offset: 0
Links
- Harry J. Smith, Table of n, a(n) for n = 0..200
- 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).
Programs
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Mathematica
CoefficientList[Series[(1 - 6 x + 28 x^2 - 32 x^3)/((1 - x) (1 - 4 x)^2), {x, 0, 21}], x] (* Michael De Vlieger, Jan 04 2020 *) -
PARI
a(n) = { abs(n*4^n - 1) } \\ Harry J. Smith, Jul 04 2009
Formula
G.f.: (1 - 6*x + 28*x^2 - 32*x^3)/((1 - x)*(1 - 4*x)^2). - Colin Barker, Apr 22 2012
From Elmo R. Oliveira, May 05 2025: (Start)
E.g.f.: 2 + exp(x)*(4*x*exp(3*x) - 1).
a(n) = A018215(n) - 1 for n >= 1.
a(n) = 9*a(n-1) - 24*a(n-2) + 16*a(n-3) for n > 3. (End)