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A199301
a(n) = (2n+1)*8^n.
4
1, 24, 320, 3584, 36864, 360448, 3407872, 31457280, 285212672, 2550136832, 22548578304, 197568495616, 1717986918400, 14843406974976, 127543348822016, 1090715534753792, 9288674231451648, 78812993478983680, 666532744850833408, 5620492334958379008, 47269781688880726016
OFFSET
0,2
FORMULA
a(n) = 16*a(n-1)-64*a(n-2).
G.f.: (1+8*x)/(1-8*x)^2.
a(n) = 8*(a(n-1)+2^(3*n-2)). - Vincenzo Librandi, Nov 05 2011
a(n) = A005408(n) * A001018(n). - Wesley Ivan Hurt, Oct 30 2014
From Amiram Eldar, Dec 10 2022: (Start)
Sum_{n>=0} 1/a(n) = sqrt(8)*arccoth(sqrt(8)).
Sum_{n>=0} (-1)^n/a(n) = sqrt(8)*arccot(sqrt(8)). (End)
E.g.f.: exp(8*x)*(1 + 16*x). - Stefano Spezia, May 09 2023
MAPLE
A199301:=n->(2*n+1)*8^n: seq(A199301(n), n=0..20); # Wesley Ivan Hurt, Oct 30 2014
MATHEMATICA
Table[(2 n + 1)*8^n, {n, 0, 20}] (* Wesley Ivan Hurt, Oct 30 2014 *)
PROG
(Magma) [(2*n+1)*8^n: n in [0..30]]; // Vincenzo Librandi, Nov 05 2011
(PARI) a(n) = (2*n+1)*8^n \\ Amiram Eldar, Dec 10 2022
CROSSREFS
Cf. A001018 (Powers of 8), A005408 (2n+1).
Sequence in context: A319554 A069779 A288507 * A239793 A289706 A300846
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Nov 04 2011
EXTENSIONS
a(18) corrected by Vincenzo Librandi, Nov 05 2011
STATUS
approved