OFFSET
0,4
COMMENTS
This sequence interlaced with its self-convolution yields the original sequence.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
FORMULA
a(2^k) = 1 and a(2^k*n) = a(n), with a(0) = 1, for k>=0 and n>=0.
a(2^n-1) = A211604(n) for n>=0.
EXAMPLE
a(0)=1, a(2^k)=1, a(3*2^k)=2, a(5*2^k)=3, a(7*2^k)=6, a(9*2^k)=7, for k>=0.
Self-convolution of [1,1,1,2,1,3,2,6,1,7,3,12,2,16,...] = [1,2,3,6,7,12,16,...], which forms the terms found at odd-indexed positions.
MATHEMATICA
For[A = 1; n = 1, n <= 65, n++, A = (Normal[A] /. x -> x^2) + x*(Normal[A] /. x -> x^2)^2 + O[x]^n]; CoefficientList[A, x] (* Jean-François Alcover, Mar 06 2013, updated Apr 23 2016 *)
PROG
(Haskell)
import Data.List (transpose)
a073711 n = a073711_list !! n
a073711_list = 1 :
(tail $ concat $ transpose [a073711_list, a073712_list])
-- Reinhard Zumkeller, Dec 20 2012
(PARI) a(n)=local(A=1); for(i=0, #binary(n), A=subst(A, x, x^2+x*O(x^n))+x*subst(A, x, x^2+x*O(x^n))^2); polcoeff(A, n)
for(n=0, 65, print1(a(n), ", ")) \\ Paul D. Hanna, Dec 21 2012
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
Paul D. Hanna, Aug 05 2002
EXTENSIONS
Name changed and entry revised by Paul D. Hanna, Dec 21 2012
STATUS
approved