cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A092093 Back and Forth Summant S(n, 5): a(n) = sum{i = 0..floor(2n/5)} n-5i.

Original entry on oeis.org

1, 2, 1, 3, 0, 3, 6, 2, 6, 0, 5, 10, 3, 9, 0, 7, 14, 4, 12, 0, 9, 18, 5, 15, 0, 11, 22, 6, 18, 0, 13, 26, 7, 21, 0, 15, 30, 8, 24, 0, 17, 34, 9, 27, 0, 19, 38, 10, 30, 0, 21, 42, 11, 33, 0, 23, 46, 12, 36, 0, 25, 50, 13, 39, 0, 27, 54, 14, 42, 0, 29, 58, 15, 45, 0, 31, 62, 16, 48, 0, 33
Offset: 1

Views

Author

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

Keywords

References

  • J. Dezert, editor, Smarandacheials, Mathematics Magazine, Aurora, Canada, No. 4/2004.
  • F. Smarandache, Back and Forth Factorials, Arizona State Univ., Special Collections, 1972.
  • F. Smarandache, Back and Forth Summants, Arizona State Univ., Special Collections, 1972.

Crossrefs

Other values of k: A000004 (k = 1, 2), A092092 (k = 3), A027656 (k = 4).

Programs

  • PARI
    S(n, k=5) = local(s, x); s = n; x = n - k; while (x >= -n, s = s + x; x = x - k); s;

Formula

a(5n) = 0; a(5n+1) = 2n+1; a(5n+2) = 4n+2; a(5n+3) = n+1; a(5n+4) = 3n+3.
G.f.: x*(2*x^6+x^5+3*x^3+x^2+2*x+1) / ((x-1)^2*(x^4+x^3+x^2+x+1)^2). - Colin Barker, Jul 28 2013

Extensions

Edited and extended by David Wasserman, Dec 19 2005

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

Original entry on oeis.org

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

Views

Author

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

Keywords

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.

Crossrefs

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
Showing 1-2 of 2 results.