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A131717 Natural numbers A000027 with 6n+4 and 6n+5 terms swapped. 2
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 (list; graph; refs; listen; history; text; internal format)
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) = Sum_{k=0..n}{(1/30)*[7*(k mod 6)-13*((k+1) mod 6)+17*((k+2) mod 6)-3*((k+3) mod 6)+2*((k+4) mod 6)+2*((k+5) mod 6)]}, with n>=0. - Paolo P. Lava, Jan 31 2008

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

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Last modified April 3 17:03 EDT 2020. Contains 333197 sequences. (Running on oeis4.)