A173564 a(n) = a(n-1) + a(n-2) - [a(n-3)/4] - [a(n-4)/2] - [a(n-5)/4].

1, 1, 2, 3, 5, 8, 12, 18, 26, 36, 50, 68, 92, 124, 165, 220, 291, 385, 508, 670, 882, 1161, 1526, 2005, 2633, 3457, 4536, 5952, 7807, 10239, 13426, 17604, 23080, 30258, 39665, 51995, 68155, 89335, 117096, 153480, 201168, 263669, 345586, 452949, 593664, 778091, 1019808, 1336613, 1751830, 2296030, 3009281

Offset

0,3

Comments

The limiting ratio a(n+1)/a(n) at the 500th iteration is:1.3106397635502627

Links

Table of n, a(n) for n=0..50.

Formula

a(n)=a(n-1)+a(n-2)-Floor[a(n-3)/4]-Floor[a(n-4)/2]-Floor[a(n-5)/4]

Mathematica

f[-3] = 0; f[-2] = 0; f[-1] = 0; f[0] = 1; f[1] = 1;
f[n_] := f[n] = f[n - 1] + f[n - 2] - Floor[f[n - 3]/
4] - Floor[f[n - 4]/2] - Floor[f[n - 5]/4]
Table[f[n], {n, 0, 50}]
RecurrenceTable[{a[0]==a[1]==1, a[2]==2, a[3]==3, a[4]==5, a[n]== a[n-1]+ a[n-2]- Floor[a[n-3]/4]-Floor[a[n-4]/2]-Floor[a[n-5]/4]}, a, {n, 50}] (* Harvey P. Dale, May 18 2021 *)

Crossrefs

Cf. A173538

Sequence in context: A252864 A039899 A039901 * A121946 A241823 A058984

Adjacent sequences: A173561 A173562 A173563 * A173565 A173566 A173567

Keyword

nonn

Author

Roger L. Bagula, Nov 23 2010

Status

approved