A092092 - OEIS

%I #26 Jun 04 2020 09:25:03

%S 1,1,0,3,2,0,5,3,0,7,4,0,9,5,0,11,6,0,13,7,0,15,8,0,17,9,0,19,10,0,21,

%T 11,0,23,12,0,25,13,0,27,14,0,29,15,0,31,16,0,33,17,0,35,18,0,37,19,0,

%U 39,20,0,41,21,0,43,22,0,45,23,0,47,24,0,49,25,0,51,26,0,53,27,0,55,28

%N Back and Forth Summant S(n, _3): a(n) = Sum_{i=0..floor(2n/3)} (n-3i).

%C The terms for n>1 can also be defined by: a(n)=0 if n==0 (mod 3), and otherwise a(n) equals the inverse of 3 in Z/nZ*. - _José María Grau Ribas_, Jun 18 2013

%C The subsequence of nonzero terms is essentially the same as A026741. - _Giovanni Resta_, Jun 18 2013

%D F. Smarandache, Back and Forth Summants, Arizona State Univ., Special Collections, 1972.

%H Robert Israel, <a href="/A092092/b092092.txt">Table of n, a(n) for n = 1..10000</a>

%H J. Dezert, editor, <a href="http://www.mathematicsmagazine.com/corresp/J_Dezert/JDezert.htm">Smarandacheials</a>, Mathematics Magazine, Aurora, Canada

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).

%F a(3n) = 0; a(3n+1) = 2n+1; a(3n+2) = n+1.

%F G.f.: x*(1+x+x^3) / ( (x-1)^2*(1+x+x^2)^2 ). - _R. J. Mathar_, Jun 26 2013

%F a(n) = Sum_{k=1..n} k*( floor((3k-1)/n)-floor((3k-2)/n) ). - _Anthony Browne_, May 17 2016

%p f:= proc(n) local t;

%p t:= n mod 3;

%p if t = 0 then 0 elif t = 1 then 2/3*(n+1/2) else (n+1)/3 fi

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, May 19 2016

%t LinearRecurrence[{0, 0, 2, 0, 0, -1}, {1, 1, 0, 3, 2, 0}, 100] (* _Jean-François Alcover_, Jun 04 2020 *)

%o (PARI) S(n, k=3) = local(s, x); s = n; x = n - k; while (x >= -n, s = s + x; x = x - k); s;

%Y Cf. A092094, A092397.

%Y Other values of k: A000004 (k = 1, 2), A027656 (k = 4), A092093 (k = 5).

%Y Cf. A226782 - A226787 for inverses of 4,5,6,.. in Z/nZ*.

%K nonn,easy

%O 1,4

%A Jahan Tuten (jahant(AT)indiainfo.com), Mar 29 2004

%E Edited and extended by _David Wasserman_, Dec 19 2005