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

11, 12, 20, 20, 30, 31, 32, 45, 45, 60, 61, 62, 80, 80, 100, 101, 102, 125, 125, 150, 151, 152, 180, 180, 210, 211, 212, 245, 245, 280, 281, 282, 320, 320, 360, 361, 362, 405, 405, 450, 451, 452, 500, 500, 550, 551, 552, 605, 605, 660, 661, 662, 720, 720, 780

Offset: 6

Author

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

Keywords

• nonn

References

• F. Smarandache, Back and Forth Factorials, Arizona State Univ., Special Collections, 1972.
• F. Smarandache, Back and Forth Summants, Arizona State Univ., Special Collections, 1972.

Links

• J. Dezert, ed., Smarandacheials (1), Mathematics Magazine for Grades 1-12, No. 4, 2004.
• J. Dezert, ed., Smarandacheials (2), Mathematics Magazine for Grades 1-12, No. 4, 2004.
• F. Smarandache, Summants [Broken link]

Crossrefs

Cf. A001044, A092396, A092397, A092398, A092399, A092971, A092972, A092973, A092974.

Programs

Maple

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

Mathematica

a[n_] := Sum[Abs[n-5i], {i, 0, Quotient[2n, 5]}];
Table[a[n], {n, 6, 60}] (* Jean-François Alcover, Apr 29 2023 *)

Formula

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

Extensions

Edited and extended by R. J. Mathar, Feb 01 2008

Revised by N. J. A. Sloane, Jul 03 2017