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A266084 Expansion of (5 - x - x^2 - x^3 - x^4 + 4*x^5)/( x^6 - x^5 - x + 1). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Invert blocks of five in the sequence of natural numbers.
LINKS
Eric Weisstein's World of Mathematics, Natural Number
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
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 *)
PROG
(Magma) [5+5*Floor(n/5)-n mod 5: n in [0..70]]; // Vincenzo Librandi, Dec 21 2015
(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
CROSSREFS
Sequence in context: A071691 A319332 A031017 * A055116 A276373 A317173
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Dec 21 2015
STATUS
approved

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Last modified February 21 18:07 EST 2024. Contains 370237 sequences. (Running on oeis4.)