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A229135
n * (2 + 2^(2*n - 1)).
2
0, 4, 20, 102, 520, 2570, 12300, 57358, 262160, 1179666, 5242900, 23068694, 100663320, 436207642, 1879048220, 8053063710, 34359738400, 146028888098, 618475290660, 2611340116006, 10995116277800, 46179488366634, 193514046488620, 809240558043182, 3377699720527920
OFFSET
0,2
COMMENTS
a(n) mod 9 is periodic: repeat 0, 4, 2, 3, 7, 5, 6, 1, 8.
b(n) = a(n) - n = 0, 3, 18, 99, 516, 2565, 12294,... = A215149(2n)/2.
FORMULA
a(n) = n + A215149(2n)/2.
a(n) = (A228827(n) - A000367(n))/A002445(n).
a(n) = 2*n*A123166(n).
G.f.: (34*x^3 - 20*x^2 + 4*x)/((1-x)^2*(1-4*x)^2). - Ralf Stephan, Sep 20 2013
EXAMPLE
a(0)=0*(2+1/2)=0, a(1)=1*(2+2)=4, a(2)=2*(2+8)=20, a(3)=3*(2+32)=102, a(4)=4*(2+128)=520, a(5)=5*(2+512)=2570.
MATHEMATICA
Table[(n (2 + 2^(2 n - 1))), {n, 0, 40}] (* Vincenzo Librandi, Sep 20 2013 *)
PROG
(PARI) a(n) = n*(2+2^(2*n-1)); \\ Michel Marcus, Sep 16 2013
(Magma) [n*(2 + 2^(2*n - 1)): n in [0..30]]; // Vincenzo Librandi, Sep 20 2013
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Sep 15 2013
EXTENSIONS
Better definition by Michel Marcus.
More terms from Vincenzo Librandi, Sep 20 2013
STATUS
approved