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

%I A092093 #11 Jan 05 2025 23:38:18
%S A092093 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,
%T A092093 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,
%U A092093 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
%N A092093 Back and Forth Summant S(n, _5): a(n) = sum_{i = 0..floor(2n/5)} n-5i.
%D A092093 J. Dezert, editor, Smarandacheials, Mathematics Magazine, Aurora, Canada, No. 4/2004.
%D A092093 F. Smarandache, Back and Forth Factorials, Arizona State Univ., Special Collections, 1972.
%D A092093 F. Smarandache, Back and Forth Summants, Arizona State Univ., Special Collections, 1972.
%H A092093 J. Dezert, <a href="http://www.gallup.unm.edu/~smarandache/Smarandacheials.htm">Smaran dacheials</a>
%H A092093 J. Dezert, <a href="http://www.mathematicsmagazine.com/corresp/J_Dezert/JDezert.htm">S marandacheials, "Mathematics Magazine", Canada</a>
%H A092093 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/Summants.htm">Summants</a>
%H A092093 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,2,0,0,0,0,-1).
%F A092093 a(5n) = 0; a(5n+1) = 2n+1; a(5n+2) = 4n+2; a(5n+3) = n+1; a(5n+4) = 3n+3.
%F A092093 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
%o A092093 (PARI) S(n, k=5) = local(s, x); s = n; x = n - k; while (x >= -n, s = s + x; x = x - k); s;
%Y A092093 Cf. A092096, A092399.
%Y A092093 Other values of k: A000004 (k = 1, 2), A092092 (k = 3), A027656 (k = 4).
%K A092093 nonn,easy
%O A092093 1,2
%A A092093 Jahan Tuten (jahant(AT)indiainfo.com), Mar 29 2004
%E A092093 Edited and extended by _David Wasserman_, Dec 19 2005