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%I #19 Apr 05 2020 04:58:37
%S 7,12,18,19,27,36,37,48,60,61,75,90,91,108,126,127,147,168,169,192,
%T 216,217,243,270,271,300,330,331,363,396,397,432,468,469,507,546,547,
%U 588,630,631,675,720,721,768,816,817,867,918,919,972,1026,1027,1083,1140
%N a(n) = Sum_{i=0,1,2,..; n-k*i >= -n} |n-k*i| for k=3.
%D F. Smarandache, Back and Forth Factorials, Arizona State Univ., Special Collections, 1972.
%D F. Smarandache, Back and Forth Summants, Arizona State Univ., Special Collections, 1972.
%H J. Dezert, ed., <a href="http://www.mathematicsmagazine.com/corresp/J_Dezert/JDezert.htm">Smarandacheials (1)</a>, Mathematics Magazine for Grades 1-12, No. 4, 2004.
%H J. Dezert, ed., <a href="http://www.mathematicsmagazine.com/corresp/J_Dezert/JDezert2.htm">Smarandacheials (2)</a>, Mathematics Magazine for Grades 1-12, No. 4, 2004.
%H F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/Summants.htm">Summants</a> [Broken link]
%F S_abs(n, 3) = Sigma_{i=0, 1, 2, ...}_{0<abs(n-3i)<=n}(abs(n-3i)) = n+abs(n-3)+abs(n-6)+ ...
%F Empirical g.f.: -x^4*(6*x^6-3*x^5-2*x^4-13*x^3+6*x^2+5*x+7) / ((x-1)^3*(x^2+x+1)^2). - _Colin Barker_, Jul 28 2013
%e S_abs(7, 3) = 7+abs(7-3)+abs(7-6)+abs(7-9)+abs(7-12) = 7+4+1+2+5 = 19.
%p S := proc(n,k) local a,i ; a :=0 ; i := 0 ; while n-k*i >= -n do a := a+abs(n-k*i) ; i := i+1 ; od: RETURN(a) ; end: k := 3: seq(S(n,3),n=k+1..80) ; # _R. J. Mathar_, Feb 01 2008
%t S[n_, k_] := Module[{a = 0, i = 0}, While[n - k i >= -n, a += Abs[n - k i]; i++]; a];
%t Table[S[n, 3], {n, 4, 80}] (* _Jean-François Alcover_, Apr 05 2020, from Maple *)
%Y Cf. A001044, A092396, A092397, A092398, A092399, A092971, A092972, A092973, A092974.
%K nonn
%O 4,1
%A Jahan Tuten (jahant(AT)indiainfo.com), Mar 29 2004
%E Edited and extended by _R. J. Mathar_, Feb 01 2008
%E Definition clarified by _N. J. A. Sloane_, Jul 03 2017
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