A145030 Hexanacci numbers: a(n)=a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6), {0,1,2,3,4,5...}.

0, 1, 2, 3, 4, 5, 15, 30, 59, 116, 229, 454, 903, 1791, 3552, 7045, 13974, 27719, 54984, 109065, 216339, 429126, 851207, 1688440, 3349161, 6643338, 13177611, 26138883, 51848640, 102846073, 204003706, 404658251, 802673164, 1592168717, 3158198551

Offset

1,3

Links

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

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

Formula

G.f.: x^2*(5*x^4+2*x^3-x-1) / (x^6+x^5+x^4+x^3+x^2+x-1). - Colin Barker, Oct 27 2014

Mathematica

a=0; b=1; c=2; d=3; e=4; f=5; lst={a, b, c, d, e, f}; Do[g=a+b+c+d+e+f; AppendTo[lst, g]; a=b; b=c; c=d; d=e; e=f; f=g, {n, 3!}]; lst
LinearRecurrence[{1, 1, 1, 1, 1, 1}, {0, 1, 2, 3, 4, 5}, 40] (* Harvey P. Dale, Mar 10 2016 *)

Prog

(PARI) concat(0, Vec(x^2*(5*x^4+2*x^3-x-1)/(x^6+x^5+x^4+x^3+x^2+x-1) + O(x^100))) \\ Colin Barker, Oct 27 2014

Crossrefs

Sequence in context: A201356 A183528 A145029 * A242948 A102738 A098553

Adjacent sequences: A145027 A145028 A145029 * A145031 A145032 A145033

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Sep 30 2008

Status

approved