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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
OFFSET
0,2
LINKS
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 *)
Table[n*4^n+1, {n, 0, 30}] (* or *) LinearRecurrence[{9, -24, 16}, {1, 5, 33}, 30] (* Harvey P. Dale, Sep 18 2024 *)
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