A092094 a(n) = Sum_{i=0,1,2,..; n-k*i >= -n} |n-k*i| for k=3.
7, 12, 18, 19, 27, 36, 37, 48, 60, 61, 75, 90, 91, 108, 126, 127, 147, 168, 169, 192, 216, 217, 243, 270, 271, 300, 330, 331, 363, 396, 397, 432, 468, 469, 507, 546, 547, 588, 630, 631, 675, 720, 721, 768, 816, 817, 867, 918, 919, 972, 1026, 1027, 1083, 1140
Offset: 4
Keywords
Examples
S_abs(7, 3) = 7+abs(7-3)+abs(7-6)+abs(7-9)+abs(7-12) = 7+4+1+2+5 = 19.
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]
Programs
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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
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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 *)
Formula
S_abs(n, 3) = Sigma_{i=0, 1, 2, ...}_{0
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
Extensions
Edited and extended by R. J. Mathar, Feb 01 2008
Definition clarified by N. J. A. Sloane, Jul 03 2017