A036564 a(n) = 2^n - 45 with n>5, a(5)=1.

1, 19, 83, 211, 467, 979, 2003, 4051, 8147, 16339, 32723, 65491, 131027, 262099, 524243, 1048531, 2097107, 4194259, 8388563, 16777171, 33554387, 67108819, 134217683, 268435411, 536870867, 1073741779, 2147483603, 4294967251

Offset: 5

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 5..1000
• Robert Sedgewick, Analysis of shellsort and related algorithms, Fourth European Symposium on Algorithms, Barcelona, September, 1996.
• Index entries for linear recurrences with constant coefficients, signature (3,-2).
• Index entries for sequences related to sorting

Crossrefs

Sequences used for Shell sort: this sequence, A003462, A033622, A036562, A036569, A055875.

Programs

Mathematica

A036564[n_]:=If[n>5,2^n-45,1];Array[A036564,50,5] (* or *)
LinearRecurrence[{3,-2},{1,19,83},50] (* Paolo Xausa, Dec 03 2023 *)

PARI

a(n)=if(n>5,2^n-45,1) \\ Charles R Greathouse IV, Mar 10 2012

Python

def a(n): return pow(2, n)-45 if n!= 5 else 1
for n in range(5, 100): print(a(n), end=', ') # Javier Rivera Romeu, Mar 04 2022

Formula

G.f.: x^5*(1+2*x)*(1+14*x)/((1-x)*(1-2*x)). [Colin Barker, Mar 09 2012]