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

4,1

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=4..57.

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

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

Sequence in context: A183046 A272785 A272808 * A064665 A369357 A142337

Adjacent sequences: A092091 A092092 A092093 * A092095 A092096 A092097

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