A397213 G.f. A(x) satisfies (1-2*x)*A(x) + A(x^4) = x.

1, 2, 4, 7, 14, 28, 56, 110, 220, 440, 880, 1756, 3512, 7024, 14048, 28089, 56178, 112356, 224712, 449410, 898820, 1797640, 3595280, 7190532, 14381064, 28762128, 57524256, 115048456, 230096912, 460193824, 920387648, 1840775186, 3681550372, 7363100744, 14726201488

Offset

1,2

Links

Table of n, a(n) for n=1..35.

Formula

G.f.: Sum_{j>=0} (-1)^j*x^(4^j) / Product_{k=0..j} (1 - 2*x^(4^k)).

a(1) = 1; for n >= 2, a(n) = 2*a(n-1) - a(n/4) if 4|n, and a(n) = 2*a(n-1) otherwise.

a(n) = 2^(n-1) - Sum_{k=1..floor(n/4)} 2^(n-4*k) * a(k).

Prog

(Ruby)
def A397213(n)
  a = [0]
  (1..n).each{|i|
  a << (1..i / 4).inject(2 ** (i - 1)){|s, k| s - 2 ** (i - 4 * k) * a[k]}}
  a[1..-1]
end
p A397213(40)

Crossrefs

Cf. A045690, A397064, A398036.

Sequence in context: A358837 A251653 A057744 * A251708 A293325 A251713

Adjacent sequences: A397208 A397209 A397212 * A397215 A397216 A397218

Keyword

nonn,new

Author

Seiichi Manyama, Jul 17 2026

Status

approved