A265672 a(n) = n + floor((n+1)/7)*(-1)^((n+1) mod 7).

0, 1, 2, 3, 4, 5, 7, 6, 9, 8, 11, 10, 13, 15, 12, 17, 14, 19, 16, 21, 23, 18, 25, 20, 27, 22, 29, 31, 24, 33, 26, 35, 28, 37, 39, 30, 41, 32, 43, 34, 45, 47, 36, 49, 38, 51, 40, 53, 55, 42, 57, 44, 59, 46, 61, 63, 48, 65, 50, 67, 52, 69, 71, 54, 73, 56, 75

Offset

0,3

Comments

A permutation of A001477. This sequence, without the terms of the form 8*k+5, becomes A265228.

Similar sequences of the type n + floor((n+1)/k)*(-1)^((n+1) mod k):

k = 1: A005408;

k = 2: A014682;

k = 3: A006369 (permutation of A001477);

k = 4: 0, 1, 2, 4, 3, 6, 5, 9, 6, 11, 8, 14, ...;

k = 5: 0, 1, 2, 3, 5, 4, 7, 6, 9, 11, 8, 13, ... (permutation of A001477);

k = 6: 0, 1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 13, ...;

k = 7: this sequence.

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

Formula

a(n) = a(n-7) + (-1)^((n+1) mod 7) + 7 for n>6.

From Colin Barker, Dec 13 2015: (Start)

a(n) = 2*a(n-7) - a(n-14) for n>13.

G.f.: x*(1 +x^2)*(1 +2*x +2*x^2 +2*x^3 +3*x^4 +5*x^5 +3*x^6 +2*x^7 +x^8 +3*x^9 +x^10) / ((1 -x)^2*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6)^2). (End)

Example

-------------------------------------------------------------------------
0, 1, 2, 3, 4, 5, 6,  7, 8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, ...
+  +  +  +  +  +  +   +  +   +   +   +   +   +   +   +   +   +   +
0, 0, 0, 0, 0, 0, 1, -1, 1, -1,  1, -1,  1,  2, -2,  2, -2,  2, -2, ...
-------------------------------------------------------------------------
0, 1, 2, 3, 4, 5, 7,  6, 9,  8, 11, 10, 13, 15, 12, 17, 14, 19, 16, ...
-------------------------------------------------------------------------

Maple

A265672:=n->n + floor((n+1)/7)*(-1)^((n+1) mod 7): seq(A265672(n), n=0..100); # Wesley Ivan Hurt, Apr 09 2017

Mathematica

Table[n + Floor[(n + 1)/7] (-1)^Mod[n + 1, 7], {n, 0, 80}] (* Bruno Berselli, Dec 22 2015 *)

Prog

(PARI) concat(0, Vec(x*(1 +x^2)*(1 +2*x +2*x^2 +2*x^3 +3*x^4 +5*x^5 +3*x^6 +2*x^7 +x^8 +3*x^9 +x^10) / ((1 -x)^2*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6)^2) + O(x^100))) \\ Colin Barker, Dec 13 2015
(Magma) [n+Floor((n+1)/7)*(-1)^((n+1) mod 7): n in [0..80]]; // Bruno Berselli, Dec 26 2015

Crossrefs

Cf. A001477, A006369, A265228, A265667, A265734.

Sequence in context: A209637 A347540 A120750 * A178528 A183084 A185975

Adjacent sequences: A265669 A265670 A265671 * A265673 A265674 A265675

Keyword

nonn,easy

Author

Paul Curtz, Dec 13 2015

Extensions

Edited by Bruno Berselli, Dec 22 2015

Status

approved