OFFSET
1,3
LINKS
Robert Israel, Table of n, a(n) for n = 1..1650
FORMULA
a(n) = a(n-1) A007400(n) + a(n-2). - Robert Israel, Jun 14 2016
MAPLE
a007400:= proc(n) option remember; local n8, n16;
n8:= n mod 8;
if n8 = 0 or n8 = 3 then return 2
elif n8 = 4 or n8 = 7 then return 4
elif n8 = 1 then return procname((n+1)/2)
elif n8 = 2 then return procname((n+2)/2)
fi;
n16:= n mod 16;
if n16 = 5 or n16 = 14 then return 4
elif n16 = 6 or n16 = 13 then return 6
fi
end proc:
a007400(0):= 0: a007400(1):= 1: a007400(2):= 4:
A[1]:= 1: A[2]:= 1:
for n from 3 to 100 do
A[n]:= A[n-1]*a007400(n-1)+A[n-2];
od:
seq(A[n], n=1..100); # Robert Israel, Jun 14 2016
MATHEMATICA
(* b is a007400 *)
b[n_] := b[n] = Module[{n8, n16}, n8 = Mod[n, 8]; Which[n8 == 0 || n8 == 3, Return[2], n8 == 4 || n8 == 7, Return[4], n8 == 1, Return[b[(n+1)/2]], n8 == 2, Return[b[(n+2)/2]]]; n16 = Mod[n, 16]; Which[n16 == 5 || n16 == 14, Return[4], n16 == 6 || n16 == 13, Return[6]]];
b[0] = 0; b[1] = 1; b[2] = 4;
a[1] = a[2] = 1;
a[n_] := a[n] = a[n-1] b[n-1] + a[n-2];
Array[a, 100] (* Jean-François Alcover, Jun 10 2020, after Robert Israel *)
PROG
(PARI) a(n)=component(component(contfracpnqn(contfrac(sum(k=0, 20, 1/2^(2^k)), n)), 1), 2)
CROSSREFS
KEYWORD
easy,frac,nonn
AUTHOR
Benoit Cloitre, Aug 23 2002
STATUS
approved