A120562 -id:A120562 - cp's OEIS frontend

A214127 a(2n) = a(n-1) + a(n) and a(2n+1) = a(n+1) for n>=1, with a(0)=1, a(1)=2.

1, 2, 3, 3, 5, 3, 6, 5, 8, 3, 8, 6, 9, 5, 11, 8, 13, 3, 11, 8, 11, 6, 14, 9, 15, 5, 14, 11, 16, 8, 19, 13, 21, 3, 16, 11, 14, 8, 19, 11, 19, 6, 17, 14, 20, 9, 23, 15, 24, 5, 20, 14, 19, 11, 25, 16, 27, 8, 24, 19, 27, 13, 32, 21, 34, 3, 24, 16, 19, 11, 27, 14, 25

Offset: 0

Alex Ratushnyak, Jul 04 2012

Cf. A120562: same formula, seed {0,1}, first term removed.
Cf. A082498: same formula, seed {1,0}, first term removed.
Cf. A214126: same formula, seed {1,1}.

t = {1, 2}; Do[If[EvenQ[n], AppendTo[t, t[[n/2]] + t[[n/2 + 1]]], AppendTo[t, t[[(n + 3)/2]]]], {n, 2, 100}]; t (* T. D. Noe, Jul 11 2012 *)

a = [1]*(77*2)
a[1]=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=',')

A309047 Expansion of Product_{k>=0} (1 + x^(2^k) - x^(3*2^k)).

Original entry on oeis.org

1, 1, 1, 0, 1, 0, 0, -1, 1, 1, 0, -1, 0, 0, -1, -1, 1, 2, 1, 0, 0, -1, -1, -1, 0, 1, 0, 0, -1, -1, -1, 0, 1, 2, 2, 1, 1, -1, 0, -1, 0, 0, -1, -1, -1, 0, -1, 0, 0, 1, 1, 1, 0, -1, 0, 0, -1, -1, -1, 0, -1, 0, 0, 1, 1, 1, 2, 1, 2, 0, 1, -1, 1, 0, -1, -2, 0, 1, -1, -1, 0, 1, 0, 0, -1, -1, -1, 0, -1, 0, 0, 1, -1, -1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, -1, -1, -1, 0, 1

Offset: 0

Ilya Gutkovskiy, Jul 09 2019

sign

Cf. A002487, A005590, A120562.

nmax = 109; CoefficientList[Series[Product[(1 + x^(2^k) - x^(3 2^k)), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
nmax = 109; A[] = 1; Do[A[x] = (1 + x - x^3) A[x^2] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], a[(n - 1)/2] - a[(n - 3)/2]]; Table[a[n], {n, 0, 109}]

G.f. A(x) satisfies: A(x) = (1 + x - x^3) * A(x^2).

a(0) = a(1) = 1; a(2*n) = a(n), a(2*n+1) = a(n) - a(n-1).

cp's OEIS Frontend

A214127 a(2n) = a(n-1) + a(n) and a(2n+1) = a(n+1) for n>=1, with a(0)=1, a(1)=2.

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