OFFSET
4,1
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
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
S_abs(n, 3) = Sigma_{i=0, 1, 2, ...}_{0<abs(n-3i)<=n}(abs(n-3i)) = n+abs(n-3)+abs(n-6)+ ...
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
EXAMPLE
S_abs(7, 3) = 7+abs(7-3)+abs(7-6)+abs(7-9)+abs(7-12) = 7+4+1+2+5 = 19.
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 := 3: seq(S(n, 3), n=k+1..80) ; # R. J. Mathar, Feb 01 2008
MATHEMATICA
S[n_, k_] := Module[{a = 0, i = 0}, While[n - k i >= -n, a += Abs[n - k i]; i++]; a];
Table[S[n, 3], {n, 4, 80}] (* Jean-François Alcover, Apr 05 2020, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jahan Tuten (jahant(AT)indiainfo.com), Mar 29 2004
EXTENSIONS
Edited and extended by R. J. Mathar, Feb 01 2008
Definition clarified by N. J. A. Sloane, Jul 03 2017
STATUS
approved