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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
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
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
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Dec 13 2015
EXTENSIONS
Edited by Bruno Berselli, Dec 22 2015
STATUS
approved