A214126 - OEIS

A214126

a(2n)=a(n-1)+a(n) and a(2n+1)=a(n+1) for n>=1, with a(0)=a(1)=1.

1, 1, 2, 2, 3, 2, 4, 3, 5, 2, 5, 4, 6, 3, 7, 5, 8, 2, 7, 5, 7, 4, 9, 6, 10, 3, 9, 7, 10, 5, 12, 8, 13, 2, 10, 7, 9, 5, 12, 7, 12, 4, 11, 9, 13, 6, 15, 10, 16, 3, 13, 9, 12, 7, 16, 10, 17, 5, 15, 12, 17, 8, 20, 13, 21, 2, 15, 10, 12, 7, 17, 9, 16, 5, 14, 12

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OFFSET

0,3

COMMENTS

a(2^n) = A000045(n+2), a(2^n-1) = A000045(n+1). - Alois P. Heinz, Jul 06 2012

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..8192

FORMULA

a(0) = a(1) = 1, for n>=1: a(2*n) = a(n-1)+a(n) and a(2*n+1) = a(n+1).

EXAMPLE

a(2^n+1) = 2 because a(2) = 2 and a(2*n+1) = a(n+1).

MAPLE

a:= proc(n) local r;

a(n):= `if`(n<2, 1, `if`(irem(n, 2, 'r')=0, a(r-1)+a(r), a(r+1)))

end:

seq(a(n), n=1..100); # Alois P. Heinz, Jul 06 2012

MATHEMATICA

a[0] = a[1] = 1;

a[n_] := a[n] = If[EvenQ[n], a[n/2-1] + a[n/2], a[(n-1)/2+1]];

Array[a, 100, 0] (* Jean-François Alcover, May 31 2019 *)

PROG

(Python)

a = [1]*(77*2)

for n in range(1, 77):

a[2*n ]=a[n-1]+a[n]

a[2*n+1]=a[n+1]

print(str(a[n-1]), end=', ')

CROSSREFS

Cf. A120562: same formula, seed {0,1}, first term removed.

Cf. A082498: same formula, seed {1,0}, first term removed.

Cf. A214127: same formula, seed {1,2}.

Cf. A000045.

Sequence in context: A360179 A361511 A345147 * A205378 A323889 A286378

Adjacent sequences: A214123 A214124 A214125 * A214127 A214128 A214129

KEYWORD

nonn,easy

AUTHOR

Alex Ratushnyak, Jul 04 2012

STATUS

approved