A398036 G.f. A(x) satisfies (1-3*x)*A(x) + A(x^4) = x.

1, 3, 9, 26, 78, 234, 702, 2103, 6309, 18927, 56781, 170334, 511002, 1533006, 4599018, 13797028, 41391084, 124173252, 372519756, 1117559190, 3352677570, 10058032710, 30174098130, 90522294156, 271566882468, 814700647404, 2444101942212, 7332305825934, 21996917477802

Offset

1,2

Links

Table of n, a(n) for n=1..29.

Formula

G.f.: Sum_{j>=0} (-1)^j*x^(4^j) / Product_{k=0..j} (1 - 3*x^(4^k)).

a(1) = 1; for n >= 2, a(n) = 3*a(n-1) - a(n/4) if 4|n, and a(n) = 3*a(n-1) otherwise.

a(n) = 3^(n-1) - Sum_{k=1..floor(n/4)} 3^(n-4*k) * a(k).

Prog

(Ruby)
def A398036(n)
  a = [0]
  (1..n).each{|i|
  a << (1..i / 4).inject(3 ** (i - 1)){|s, k| s - 3 ** (i - 4 * k) * a[k]}}
  a[1..-1]
end
p A398036(30)

Crossrefs

Cf. A045694, A397274.

Sequence in context: A027915 A384648 A295115 * A114982 A133405 A368088

Adjacent sequences: A398027 A398028 A398029 * A398039 A398040 A398041

Keyword

nonn,new

Author

Seiichi Manyama, Jul 18 2026

Status

approved