A266084 Expansion of (5 - x - x^2 - x^3 - x^4 + 4*x^5)/( x^6 - x^5 - x + 1).

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

Offset: 0

Author

Ilya Gutkovskiy, Dec 21 2015

Keywords

• nonn
• easy

Comments

Invert blocks of five in the sequence of natural numbers.

Links

• Eric Weisstein's World of Mathematics, Natural Number
• Index entries for permutations of the positive (or nonnegative) integers.
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Crossrefs

Cf. A000027, A113655, A113778.

Programs

Magma

[5+5*Floor(n/5)-n mod 5: n in [0..70]]; // Vincenzo Librandi, Dec 21 2015

Mathematica

Table[5 + 5 Floor[n/5] - Mod[n, 5], {n, 0, 50}]
CoefficientList[Series[(5 - x - x^2 - x^3 - x^4 + 4 x^5)/(x^6 - x^5 - x + 1), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 21 2015 *)
Reverse/@Partition[Range[80],5]//Flatten (* or *) LinearRecurrence[ {1,0,0,0,1,-1},{5,4,3,2,1,10},80] (* Harvey P. Dale, Sep 02 2016 *)

PARI

a(n) = 5 + 5*(n\5) - (n % 5); \\ Michel Marcus, Dec 21 2015

PARI

x='x+O('x^100); Vec((5-x-x^2-x^3-x^4+4*x^5)/(x^6-x^5-x+1)) \\ Altug Alkan, Dec 21 2015

Formula

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

a(n) = a(n-1) + a(n-5) - a(n-6) for n>5.

a(n) = 5 + 5*floor(n/5) - n mod 5.

a(n) = n+1+2*A257145(n+3). - R. J. Mathar, Apr 12 2019