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A092096 a(n) = Sum_{i=0,1,2,..; n-k*i >= -n} |n-k*i| for k=5.

%I A092096 #17 Apr 29 2023 09:47:38
%S A092096 11,12,20,20,30,31,32,45,45,60,61,62,80,80,100,101,102,125,125,150,
%T A092096 151,152,180,180,210,211,212,245,245,280,281,282,320,320,360,361,362,
%U A092096 405,405,450,451,452,500,500,550,551,552,605,605,660,661,662,720,720,780
%N A092096 a(n) = Sum_{i=0,1,2,..; n-k*i >= -n} |n-k*i| for k=5.
%D A092096 F. Smarandache, Back and Forth Factorials, Arizona State Univ., Special Collections, 1972.
%D A092096 F. Smarandache, Back and Forth Summants, Arizona State Univ., Special Collections, 1972.
%H A092096 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 A092096 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 A092096 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/Summants.htm">Summants</a> [Broken link]
%F A092096 Empirical g.f.: -x^6*(10*x^10-5*x^9-3*x^7-x^6-21*x^5+10*x^4+8*x^2+x+11) / ((x-1)^3*(x^4+x^3+x^2+x+1)^2). - _Colin Barker_, Jul 28 2013
%p A092096 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 := 5: seq(S(n,k),n=k+1..80) ; # _R. J. Mathar_, Feb 01 2008
%t A092096 a[n_] := Sum[Abs[n-5i], {i, 0, Quotient[2n, 5]}];
%t A092096 Table[a[n], {n, 6, 60}] (* _Jean-François Alcover_, Apr 29 2023 *)
%Y A092096 Cf. A001044, A092396, A092397, A092398, A092399, A092971, A092972, A092973, A092974.
%K A092096 nonn
%O A092096 6,1
%A A092096 Jahan Tuten (jahant(AT)indiainfo.com), Mar 29 2004
%E A092096 Edited and extended by _R. J. Mathar_, Feb 01 2008
%E A092096 Revised by _N. J. A. Sloane_, Jul 03 2017