A260644 Four steps forward, three steps back.

0, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 6, 5, 4, 5, 6, 7, 8, 7, 6, 5, 6, 7, 8, 9, 8, 7, 6, 7, 8, 9, 10, 9, 8, 7, 8, 9, 10, 11, 10, 9, 8, 9, 10, 11, 12, 11, 10, 9, 10, 11, 12, 13, 12, 11, 10, 11, 12, 13, 14, 13, 12, 11

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (a(301) = 43 corrected by Georg Fischer, Apr 10 2019 *)

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

Formula

G.f.: x*(1+x+x^2+x^3-x^4-x^5-x^6) / ((1-x)^2*(1+x+x^2+x^3+x^4+x^5+x^6)).

a(n) = a(n-1) + a(n-7) - a(n-8) for n>7.

a(n) = Sum_{i=1..n} (-1)^floor((2i - 2)/7).

Example

a(6k):   0,  2,  4,  6,  6,  6,  6,  6,  8, 10, 12, 12, 12, 12, 12, 14, ...
a(6k+1): 1,  1,  3,  5,  7,  7,  7,  7,  7,  9, 11, 13, 13, 13, 13, 13, ...
a(6k+2): 2,  2,  2,  4,  6,  8,  8,  8,  8,  8, 10, 12, 14, 14, 14, 14, ...
a(6k+3): 3,  3,  3,  3,  5,  7,  9,  9,  9,  9,  9, 11, 13, 15, 15, 15, ...
a(6k+4): 4,  4,  4,  4,  4,  6,  8, 10, 10, 10, 10, 10, 12, 14, 16, 16, ...
a(6k+5): 3,  5,  5,  5,  5,  5,  7,  9, 11, 11, 11, 11, 11, 13, 15, 17, ...

Maple

A260644:=n->add((-1)^floor((2*i-2)/7), i=1..n): seq(A260644(n), n=0..100);

Mathematica

Table[Sum[(-1)^Floor[(2 i - 2)/7], {i, n}], {n, 0, 100}]
LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 3, 2, 1}, 90] (* Harvey P. Dale, Dec 27 2023 *)

Prog

(PARI) concat(0, Vec((x+x^2+x^3+x^4-x^5-x^6-x^7)/((x-1)^2*(1+x+x^2+x^3+x^4+x^5+x^6)) + O(x^100))) \\ Altug Alkan, Nov 12 2015

Crossrefs

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

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

Sequence in context: A171456 A028356 A232244 * A073791 A350862 A030340

Adjacent sequences: A260641 A260642 A260643 * A260645 A260646 A260647

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Nov 11 2015

Status

approved