A079354 a(1)=1; a(n)=a(n-1)-1 if n is already in the sequence, a(n)=a(n-1)+3 otherwise.

1, 4, 7, 6, 9, 8, 7, 6, 5, 8, 11, 14, 17, 16, 19, 18, 17, 16, 15, 18, 21, 24, 27, 26, 29, 28, 27, 26, 25, 28, 31, 34, 37, 36, 39, 38, 37, 36, 35, 38, 41, 44, 47, 46, 49, 48, 47, 46, 45, 48, 51, 54, 57, 56, 59, 58, 57, 56, 55, 58, 61, 64, 67, 66, 69, 68, 67, 66, 65, 68, 71, 74, 77

Offset

1,2

Comments

Starting with a(1)=0 and same definition, a(n)=n+(-1)^n (cf. A004442)

Links

Table of n, a(n) for n=1..73.

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

Formula

a(n)-n is periodic with period (0, 2, 4, 2, 4, 2, 0, -2, -4, -2) of length 10.

a(10t+i) = 10t+c_i, 1<=i<=10, c_i=(1, 4, 7, 6, 9, 8, 7, 6, 5, 8). a(n) = n iff n == 1 or 7 (mod 10).

G.f.: x*(2*x^10+3*x^9-x^8-x^7-x^6-x^5+3*x^4-x^3+3*x^2+3*x+1) / (x^11-x^10-x+1). - Colin Barker, Oct 16 2013

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 4, 7, 6, 9, 8, 7, 6, 5, 8, 11}, 80] (* Harvey P. Dale, Feb 01 2015 *)

Prog

(PARI) Vec(x*(2*x^10+3*x^9-x^8-x^7-x^6-x^5+3*x^4-x^3+3*x^2+3*x+1)/(x^11-x^10-x+1) + O(x^100)) \\ Colin Barker, Oct 16 2013

Crossrefs

Sequence in context: A140877 A293904 A069286 * A354763 A255248 A122460

Adjacent sequences: A079351 A079352 A079353 * A079355 A079356 A079357

Keyword

nonn,easy

Author

Benoit Cloitre and N. J. A. Sloane, Feb 14 2003

Status

approved