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A260644 Four steps forward, three steps back.

%I A260644 #35 Aug 01 2025 05:50:18
%S A260644 0,1,2,3,4,3,2,1,2,3,4,5,4,3,2,3,4,5,6,5,4,3,4,5,6,7,6,5,4,5,6,7,8,7,
%T A260644 6,5,6,7,8,9,8,7,6,7,8,9,10,9,8,7,8,9,10,11,10,9,8,9,10,11,12,11,10,9,
%U A260644 10,11,12,13,12,11,10,11,12,13,14,13,12,11
%N A260644 Four steps forward, three steps back.
%H A260644 G. C. Greubel, <a href="/A260644/b260644.txt">Table of n, a(n) for n = 0..1000</a> (a(301) = 43 corrected by Georg Fischer, Apr 10 2019)
%H A260644 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F A260644 G.f.: x*(1+x+x^2+x^3-x^4-x^5-x^6) / ((1-x)^2*(1+x+x^2+x^3+x^4+x^5+x^6)).
%F A260644 a(n) = a(n-1) + a(n-7) - a(n-8) for n>7.
%F A260644 a(n) = Sum_{i=1..n} (-1)^floor((2i - 2)/7).
%e A260644 a(6k):   0,  2,  4,  6,  6,  6,  6,  6,  8, 10, 12, 12, 12, 12, 12, 14, ...
%e A260644 a(6k+1): 1,  1,  3,  5,  7,  7,  7,  7,  7,  9, 11, 13, 13, 13, 13, 13, ...
%e A260644 a(6k+2): 2,  2,  2,  4,  6,  8,  8,  8,  8,  8, 10, 12, 14, 14, 14, 14, ...
%e A260644 a(6k+3): 3,  3,  3,  3,  5,  7,  9,  9,  9,  9,  9, 11, 13, 15, 15, 15, ...
%e A260644 a(6k+4): 4,  4,  4,  4,  4,  6,  8, 10, 10, 10, 10, 10, 12, 14, 16, 16, ...
%e A260644 a(6k+5): 3,  5,  5,  5,  5,  5,  7,  9, 11, 11, 11, 11, 11, 13, 15, 17, ...
%p A260644 A260644:=n->add((-1)^floor((2*i-2)/7), i=1..n): seq(A260644(n), n=0..100);
%t A260644 Table[Sum[(-1)^Floor[(2 i - 2)/7], {i, n}], {n, 0, 100}]
%t A260644 LinearRecurrence[{1,0,0,0,0,0,1,-1},{0,1,2,3,4,3,2,1},90] (* _Harvey P. Dale_, Dec 27 2023 *)
%o A260644 (PARI) concat(0, Vec((x+x^2+x^3+x^4-x^5-x^6-x^7)/((x-1)^2*(1+x+x^2+x^3+x^4+x^5+x^6)) + O(x^100))) \\ _Altug Alkan_, Nov 12 2015
%Y A260644 Cf. A008611 (one step back, two steps forward).
%Y A260644 Cf. A058207 (three steps forward, two steps back).
%K A260644 nonn,easy
%O A260644 0,3
%A A260644 _Wesley Ivan Hurt_, Nov 11 2015