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A265672 a(n) = n + floor((n+1)/7)*(-1)^((n+1) mod 7). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A217266 A209637 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

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Last modified October 24 01:20 EDT 2018. Contains 316541 sequences. (Running on oeis4.)