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A036562
a(n) = 4^(n+1) + 3*2^n + 1.
16
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
Robert Sedgewick, Analysis of shellsort and related algorithms, Fourth European Symposium on Algorithms, Barcelona, September, 1996.
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
KEYWORD
nonn,easy
STATUS
approved