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%I #30 Apr 27 2024 17:21:52
%S 1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,
%T 1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,
%U 2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0
%N NW-SE diagonal sums of Riordan array A112468.
%C Matches Fibonacci-sequence, such that F(n) + a(n) and F(n) - a(n) = always even.
%C Periodic sequence with period: [1,1,2,1,1,0]. - _Philippe Deléham_, Oct 11 2011
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,-1,1).
%F a(n) = 1 + A131531(n) with inverse binomial transform: 1, 0, 1, -3, 6, -11, 21, .., a signed variant of A024495. - _R. J. Mathar_, Mar 04 2010
%F a(2n+1) = a(2n)-a(2n-1)+2, a(2n) = a(2n-1)-a(2n-2) with a(1) = a(2)=1. - _Philippe Deléham_, Oct 11 2011
%F a(n) = a(n-1)-a(n-3)+a(n-4). - _Colin Barker_, Sep 26 2014
%F G.f.: -x*(x^2+1) / ((x-1)*(x+1)*(x^2-x+1)). - _Colin Barker_, Sep 26 2014
%F a(n) = 2*ceiling(n/6)-2*floor(n/6)+floor(n/3)-ceiling(n/3). - _Wesley Ivan Hurt_, Sep 27 2014
%F a(n) = A001045(n) - A111927(n). - _Paul Curtz_, Dec 16 2020
%p A173432:=n->2*ceil(n/6)-2*floor(n/6)+floor(n/3)-ceil(n/3): seq(A173432(n), n=1..100); # _Wesley Ivan Hurt_, Sep 27 2014
%t Table[2 Ceiling[n/6] - 2 Floor[n/6] + Floor[n/3] - Ceiling[n/3], {n, 50}] (* _Wesley Ivan Hurt_, Sep 27 2014 *)
%o (PARI) Vec(-x*(x^2+1) / ((x-1)*(x+1)*(x^2-x+1)) + O(x^100)) \\ _Colin Barker_, Sep 26 2014
%o (Magma) [2*Ceiling(n/6)-2*Floor(n/6)+Floor(n/3)-Ceiling(n/3) : n in [1..100]]; // _Wesley Ivan Hurt_, Sep 27 2014
%Y Cf. A000045, A024495, A112468, A131531.
%K nonn,easy
%O 1,3
%A _Mark Dols_, Feb 18 2010
%E Corrected and extended by _Philippe Deléham_, Oct 11 2011
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