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

Author

Paul Curtz, Dec 13 2015

Keywords

• nonn
• easy

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.

Examples

			-------------------------------------------------------------------------
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, ...
-------------------------------------------------------------------------
		

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).

Crossrefs

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

Programs

Magma

[n+Floor((n+1)/7)*(-1)^((n+1) mod 7): n in [0..80]]; // Bruno Berselli, Dec 26 2015

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 *)

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

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)

Extensions

Edited by Bruno Berselli, Dec 22 2015