A131717 Natural numbers A000027 with 6n+4 and 6n+5 terms swapped.

1, 2, 3, 5, 4, 6, 7, 8, 9, 11, 10, 12, 13, 14, 15, 17, 16, 18, 19, 20, 21, 23, 22, 24, 25, 26, 27, 29, 28, 30, 31, 32, 33, 35, 34, 36, 37, 38, 39, 41, 40, 42, 43, 44, 45, 47, 46, 48, 49, 50, 51, 53, 52, 54, 55, 56, 57, 59, 58, 60, 61, 62, 63, 65, 64, 66, 67, 68, 69, 71, 70, 72

Offset

1,2

Comments

Hexaperiodic differences: 1, 1, 2, -1, 2, 1; 0, 1, -3, 3, -1, 0 (even palindromic signed); 1,-4, 6, -4, 1, 0.

Links

Frieder Mittmann, Table of n, a(n) for n = 1..1002

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

Formula

a(n) = A008585(n/3) if n is congruent to 0 mod 3. - Frieder Mittmann, Nov 11 2014

a(n) = A007310((n-1)/3) if n is congruent to 1 mod 3. - Frieder Mittmann, Nov 11 2014

a(n) = A047235((n-2)/3) if n is congruent to 2 mod 3. - Frieder Mittmann, Nov 11 2014

G.f.: x*(2*x^5-x^4+2*x^3+x^2+x+1) / ((x-1)^2*(x+1)*(x^2-x+1)*(x^2+x+1)). - Colin Barker, Nov 11 2014

a(n) = (24*floor(n/6)-3*(n^2-3*n-2)-9*floor(n/3)*(3*floor(n/3)-2*n+3)+(-1)^floor(n/3)*(3*n^2-5*n-6+3*floor(n/3)*(9*floor(n/3)-6*n+5)))/4. - Luce ETIENNE, Apr 18 2017

Maple

seq(seq(6*i+s, s=[1, 2, 3, 5, 4, 6]), i=0..100); # Robert Israel, Nov 11 2014

Mathematica

Drop[CoefficientList[Series[x (2x^5 - x^4 + 2x^3 + x^2 + x + 1)/((x - 1)^2 (x + 1) (x^2 - x + 1) (x^2 + x + 1)), {x, 0, 100}], x], 1] (* Indranil Ghosh, Apr 18 2017 *)
Table[Sum[(7 #1 - 13 #2 + 17 #3 - 3 #4 + 2 #5 + 2 #6)/30 & @@ Mod[k + Range[0, 5], 6], {k, 0, n}], {n, 0, 71}] (* Michael De Vlieger, Apr 22 2017 *)

Prog

(PARI) Vec(x*(2*x^5-x^4+2*x^3+x^2+x+1)/((x-1)^2*(x+1)*(x^2-x+1)*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Nov 11 2014

Crossrefs

Cf. A131042.

Sequence in context: A222240 A309151 A138311 * A084489 A084490 A060119

Adjacent sequences: A131714 A131715 A131716 * A131718 A131719 A131720

Keyword

nonn,easy

Author

Paul Curtz, Sep 15 2007

Status

approved