A132270 a(n) = floor((n^7-1)/(7*n^6)), which is the same as integers repeated 7 times.
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10
Offset: 1
Links
- Wolfgang Hornfeck, Chiral spiral cyclic twins. II. A two-parameter family of cyclic twins composed of discrete circle involute spirals, Acta Cryst. (2023) Vol. 79, Part 6, 570-586.
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).
Crossrefs
Programs
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Maple
A132270:=n->floor((n-1)/7); seq(A132270(n), n=1..100); # Wesley Ivan Hurt, Dec 10 2013
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Mathematica
Table[Floor[(n - 1)/7], {n, 100}] (* Wesley Ivan Hurt, Dec 10 2013 *) Table[PadRight[{},7,n],{n,0,10}]//Flatten (* or *) LinearRecurrence[ {1,0,0,0,0,0,1,-1},{0,0,0,0,0,0,0,1},100] (* Harvey P. Dale, Jun 08 2017 *) -
PARI
a(n)=(n-1)\7 \\ Charles R Greathouse IV, Dec 10 2013
Formula
a(n) = floor((n^7-n^6)/(7*n^6-6*n^5)). - Mohammad K. Azarian, Nov 08 2007
G.f.: x^8/(1-x-x^7+x^8). - Robert Israel, Feb 02 2015
a(n) = a(n-1)+a(n-7)-a(n-8). - Wesley Ivan Hurt, May 03 2021
a(n) = floor((n-1)/7). - M. F. Hasler, May 19 2021
Sum_{n>=8} (-1)^n/a(n) = log(2) (A002162). - Amiram Eldar, Sep 30 2022
Extensions
Offset corrected by Mohammad K. Azarian, Nov 19 2008