A092095 a(n) = Sum_{i=0,1,2,...; n-k*i >= -n} |n-k*i| for k=4.

9, 16, 16, 24, 25, 36, 36, 48, 49, 64, 64, 80, 81, 100, 100, 120, 121, 144, 144, 168, 169, 196, 196, 224, 225, 256, 256, 288, 289, 324, 324, 360, 361, 400, 400, 440, 441, 484, 484, 528, 529, 576, 576, 624, 625, 676, 676, 728, 729, 784, 784, 840, 841, 900, 900

Offset: 5

Author

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

Keywords

• nonn
• easy

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]
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1).

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 := 4: seq(S(n,k),n=k+1..80) ; # R. J. Mathar, Feb 01 2008 (Adapted from program for A092096 by N. J. A. Sloane, Jul 03 2017)

PARI

a(n) = ((2*n+1)*(-1)^n - 2*(-I)^n - 2*I^n + 2*n*(n+3) + 3)/8; \\ Jinyuan Wang, Apr 09 2025

Formula

G.f.: x^5*(8*x^6-4*x^5-8*x^4+x^3-9*x^2+7*x+9)/((x^2+1)*(x+1)^2*(1-x)^3). - Alois P. Heinz, Apr 09 2025

Extensions

Edited with better definition by Omar E. Pol, Dec 28 2008

Entry revised by N. J. A. Sloane, Jul 03 2017

Offset changed to 5 and more terms from Jinyuan Wang, Apr 09 2025