|
|
A116528
|
|
a(0)=0, a(1)=1, and for n>=2, a(2*n) = a(n), a(2*n+1) = 2*a(n) + a(n+1).
|
|
15
|
|
|
0, 1, 1, 3, 1, 5, 3, 7, 1, 7, 5, 13, 3, 13, 7, 15, 1, 9, 7, 19, 5, 23, 13, 29, 3, 19, 13, 33, 7, 29, 15, 31, 1, 11, 9, 25, 7, 33, 19, 43, 5, 33, 23, 59, 13, 55, 29, 61, 3, 25, 19, 51, 13, 59, 33, 73, 7, 43, 29, 73, 15, 61, 31, 63, 1, 13
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
Equals row 2 of the array in A178239, an infinite set of sequences of the form a(n) = a(2n), a(2n+1) = r*a(n) + a(n+1). - Gary W. Adamson, May 23 2010
Given an infinite lower triangular matrix M with (1, 1, 2, 0, 0, 0, ...) in every column, shifted down twice for columns k>1; lim_{n->infinity} M^n = A116528, the left-shifted vector considered as a sequence with offset 1. - Gary W. Adamson, May 05 2010
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x * Product_{k>=0} (1 + x^(2^k) + 2*x^(2^(k+1))). - Ilya Gutkovskiy, Jul 07 2019
|
|
MAPLE
|
option remember;
if n <= 1 then
n;
elif type(n, 'even') then
procname(n/2) ;
else
2* procname((n-1)/2)+procname((n+1)/2) ;
end if;
end proc:
|
|
MATHEMATICA
|
b[0]:= 0; b[1]:= 1; b[n_?EvenQ]:= b[n] = b[n/2]; b[n_?OddQ]:= b[n] = 2*b[(n-1)/2] + b[(n+1)/2]; a = Table[b[n], {n, 1, 70}]
|
|
PROG
|
(PARI) a(n) = if(n<2, n, if(n%2==0, a(n/2), 2*a((n-1)/2) + a((n+1)/2))); \\ G. C. Greubel, Jul 07 2019
(Magma)
a:=func< n | n lt 2 select n else ((n mod 2) eq 0) select Self(Round((n+1)/2)) else (2*Self(Round(n/2)) + Self(Round((n+2)/2))) >;
(Sage)
def a(n):
if (n<2): return n
elif (mod(n, 2)==0): return a(n/2)
else: return 2*a((n-1)/2) + a((n+1)/2)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|