A026730 a(8n)=n, a(8n+4)=a(8n)+a(8n+8), a(4n+2)=a(4n)+a(4n+4), a(2n+1)=a(2n)+a(2n+2).

0, 1, 1, 2, 1, 3, 2, 3, 1, 5, 4, 7, 3, 8, 5, 7, 2, 9, 7, 12, 5, 13, 8, 11, 3, 13, 10, 17, 7, 18, 11, 15, 4, 17, 13, 22, 9, 23, 14, 19, 5, 21, 16, 27, 11, 28, 17, 23, 6, 25, 19, 32, 13, 33, 20, 27, 7, 29, 22, 37, 15, 38, 23, 31, 8, 33, 25, 42, 17, 43, 26, 35, 9, 37, 28, 47, 19, 48, 29, 39, 10

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,-1).

Formula

a(n) = 2*a(n-8) - a(n-16).

G.f.: x*(1 + x + x^2)*(1 + x^2 + x^4)*(1 + x^4 + x^8)/(1 - x^8)^2. - G. C. Greubel, Oct 26 2019

Maple

seq(coeff(series(x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2, x, n+1), x, n), n = 0 .. 90); # G. C. Greubel, Oct 26 2019

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1}, {0, 1, 1, 2, 1, 3, 2, 3, 1, 5, 4, 7, 3, 8, 5, 7}, 90] (* Harvey P. Dale, May 10 2012 *)
CoefficientList[Series[x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2, {x, 0, 90}], x]

Prog

(PARI) my(x='x+O('x^90)); concat([0], Vec(x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2)) \\ G. C. Greubel, Oct 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 90); [0] cat Coefficients(R!( x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2 )); // G. C. Greubel, Oct 26 2019
(Sage)
def A026730_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2 ).list()
A026730_list(90) # G. C. Greubel, Oct 26 2019
(GAP) a:=[0, 1, 1, 2, 1, 3, 2, 3, 1, 5, 4, 7, 3, 8, 5, 7];; for n in [17..90] do a[n]:=2*a[n-8]-a[n-16]; od; a; # G. C. Greubel, Oct 26 2019

Crossrefs

Sequence in context: A263017 A245328 A060162 * A318691 A075256 A334523

Adjacent sequences: A026727 A026728 A026729 * A026731 A026732 A026733

Keyword

nonn,easy

Author

J. Carl Bellinger (carlb(AT)ctron.com)

Extensions

Shorter description and more terms from David W. Wilson

Status

approved