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

6,1

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

Table of n, a(n) for n=6..60.

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]

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

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 *)

Crossrefs

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

Sequence in context: A046465 A134926 A105744 * A057303 A121979 A109372

Adjacent sequences: A092093 A092094 A092095 * A092097 A092098 A092099

Keyword

nonn

Author

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

Extensions

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

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

Status

approved