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A050915 a(n) = n*4^n + 1. 4
1, 5, 33, 193, 1025, 5121, 24577, 114689, 524289, 2359297, 10485761, 46137345, 201326593, 872415233, 3758096385, 16106127361, 68719476737, 292057776129, 1236950581249, 5222680231937, 21990232555521, 92358976733185 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Amelia Carolina Sparavigna, Some Groupoids and their Representations by Means of Integer Sequences, International Journal of Sciences (2019) Vol. 8, No. 10.
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
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 *)
PROG
(Magma) [ n*4^n+1: n in [0..30]]; // Vincenzo Librandi, Sep 16 2011
CROSSREFS
Cf. A002064.
Sequence in context: A270726 A308679 A272833 * A091056 A244901 A197675
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 30 1999
STATUS
approved

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Last modified March 29 09:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)