A036562 a(n) = 4^(n+1) + 3*2^n + 1.

1, 8, 23, 77, 281, 1073, 4193, 16577, 65921, 262913, 1050113, 4197377, 16783361, 67121153, 268460033, 1073790977, 4295065601, 17180065793, 68719869953, 274878693377, 1099513200641, 4398049656833, 17592192335873, 70368756760577

Offset

-1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = -1..1000

Robert Sedgewick, Analysis of shellsort and related algorithms, Fourth European Symposium on Algorithms, Barcelona, September, 1996.

Index entries for sequences related to sorting

Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Formula

a(n) = (1/2)*(A028401(n+4) + 1) for n > -1.

G.f.: (1+x-19*x^2+20*x^3)/(x*(1-x)*(1-2*x)*(1-4*x)). - Colin Barker, Mar 09 2012

a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3), for n>=3. - Wesley Ivan Hurt, Apr 26 2021

Mathematica

CoefficientList[Series[x*(1+x-19*x^2+20*x^3)/(x*(1-x)*(1-2*x)*(1-4*x)), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 24 2012 *)

Prog

(Magma) [1]cat[4^(n+1)+3*2^n+1:n in [0..30]]; // Vincenzo Librandi, Apr 24 2012
(PARI) a(n)=4^(n+1)+3*2^n+1 \\ Charles R Greathouse IV, Apr 24 2012
(Python)
def a(n): return 1 if n == -1 else (pow(4, n+1)+3*pow(2, n)+1)
print([a(n) for n in range(-1, 100)]) # Javier Rivera Romeu, Mar 05 2022

Crossrefs

Sequences used for Shell sort: A003462, A033622, A036562, A036564, A036569, A055875, A055876.

Sequence in context: A059209 A099274 A208633 * A320310 A303720 A304414

Adjacent sequences: A036559 A036560 A036561 * A036563 A036564 A036565

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved