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%I #44 Dec 31 2023 10:16:49
%S 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,
%T 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,
%U 9,9,10,10,10,10,10,10
%N a(n) = floor((n^7-1)/(7*n^6)), which is the same as integers repeated 7 times.
%H Wolfgang Hornfeck, <a href="https://doi.org/10.1107/S2053273323008276">Chiral spiral cyclic twins. II. A two-parameter family of cyclic twins composed of discrete circle involute spirals</a>, Acta Cryst. (2023) Vol. 79, Part 6, 570-586.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F a(n) = floor((n^7-n^6)/(7*n^6-6*n^5)). - _Mohammad K. Azarian_, Nov 08 2007
%F G.f.: x^8/(1-x-x^7+x^8). - _Robert Israel_, Feb 02 2015
%F a(n) = a(n-1)+a(n-7)-a(n-8). - _Wesley Ivan Hurt_, May 03 2021
%F a(n) = floor((n-1)/7). - _M. F. Hasler_, May 19 2021
%F Sum_{n>=8} (-1)^n/a(n) = log(2) (A002162). - _Amiram Eldar_, Sep 30 2022
%p A132270:=n->floor((n-1)/7); seq(A132270(n), n=1..100); # _Wesley Ivan Hurt_, Dec 10 2013
%t Table[Floor[(n - 1)/7], {n, 100}] (* _Wesley Ivan Hurt_, Dec 10 2013 *)
%t 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 *)
%o (PARI) a(n)=(n-1)\7 \\ _Charles R Greathouse IV_, Dec 10 2013
%Y Cf. A004526 ([n/2]), A002264 ([n/3]), A002265 ([n/4]), A002266 ([n/5]), A054895.
%Y Cf. A152467 ([n/6]), A132292 ([(n-1)/8]).
%Y Cf. A002162.
%K nonn,easy
%O 1,15
%A _Mohammad K. Azarian_, Nov 06 2007
%E Offset corrected by _Mohammad K. Azarian_, Nov 19 2008
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