A265228 Interleave the even numbers with the numbers that are congruent to {1, 3, 7} mod 8.

0, 1, 2, 3, 4, 7, 6, 9, 8, 11, 10, 15, 12, 17, 14, 19, 16, 23, 18, 25, 20, 27, 22, 31, 24, 33, 26, 35, 28, 39, 30, 41, 32, 43, 34, 47, 36, 49, 38, 51, 40, 55, 42, 57, 44, 59, 46, 63, 48, 65, 50, 67, 52, 71, 54, 73, 56, 75, 58, 79, 60, 81, 62, 83, 64, 87, 66

Offset

0,3

Comments

b(n) denotes the sequence:

0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1, 1, 2, -2, 2, -2, 2, -2, 2, 3, -3, 3, -3, 3, -3, 3, 4, -4, ..., and

c(n) = n + b(n) = n + floor((n+1)/7)*(-1)^((n+1) mod 7) provides:

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, ..., which is a permutation of A001477.

a(n) differs from c(n) because c(n) contains the terms of the form 8*k+5.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = n + 2*A260160(n) = n + (1-(-1)^n)*floor(n/6+1/3). Therefore, for odd n, a(n) = A047529((n+1)/2); otherwise, a(n) = n.

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

a(n) = A260708(n) - A260699(n-1) - A079979(n+3), with A260699(-1) = 0.

From Colin Barker, Dec 06 2015: (Start)

a(n) = a(n-2) + a(n-6) - a(n-8) for n > 7.

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

Mathematica

lim = 11; Riffle[Range[0, 6 lim, 2], Select[Range[8 lim], MemberQ[{1, 3, 7}, Mod[#, 8]] &]] (* Michael De Vlieger, Dec 06 2015 *)

Prog

(PARI) concat(0, Vec(x*(1+2*x+2*x^2+2*x^3+4*x^4+2*x^5+x^6)/((1-x)^2 *(1+x)^2*(1-x+x^2)*(1+x+x^2)) + O(x^100))) \\ Colin Barker, Dec 06 2015
(PARI) vector(100, n, n--; n+(1-(-1)^n)*floor(n/6+1/3)) \\ Altug Alkan, Dec 09 2015

Crossrefs

Cf. A001477, A004770, A005843, A047529, A079979, A260160, A260699, A260708.

Sequence in context: A260436 A255553 A260742 * A328877 A125595 A091202

Adjacent sequences: A265225 A265226 A265227 * A265229 A265230 A265231

Keyword

nonn,easy

Author

Paul Curtz, Dec 06 2015

Status

approved