A271800 Five steps forward, four steps back.

0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 9, 10, 11, 12, 13, 12, 11, 10

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = a(n-1) + a(n-9) - a(n-10) for n>9.

a(n) = Sum_{i=1..n} (-1)^floor((2*i-2)/9).

G.f.: x*(1+x+x^2+x^3+x^4-x^5-x^6-x^7-x^8) / ((1-x)^2*(1+x+x^2)*(1+x^3+x^6)). - Colin Barker, Apr 15 2016

Maple

A271800:=n->add((-1)^floor((2*i-2)/9), i=1..n): seq(A271800(n), n=0..200);

Mathematica

Table[Sum[(-1)^Floor[(2 i - 2)/9], {i, n}], {n, 0, 100}]

Prog

(PARI) concat(0, Vec(x*(1+x+x^2+x^3+x^4-x^5-x^6-x^7-x^8)/((1-x)^2*(1+x+x^2)*(1+x^3+x^6)) + O(x^50))) \\ Colin Barker, Apr 15 2016

Crossrefs

Cf. A008611 (one step back, two steps forward).

Cf. A058207 (three steps forward, two steps back).

Cf. A260644 (four steps forward, three steps back).

Sequence in context: A131974 A181975 A062406 * A073792 A017870 A017860

Adjacent sequences: A271797 A271798 A271799 * A271801 A271802 A271803

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 15 2016

Status

approved