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%I #21 Feb 14 2023 08:58:26
%S 1,-1,1,-2,2,-2,3,-3,3,-4,4,-4,5,-5,5,-6,6,-6,7,-7,7,-8,8,-8,9,-9,9,
%T -10,10,-10,11,-11,11,-12,12,-12,13,-13,13,-14,14,-14,15,-15,15,-16,
%U 16,-16,17,-17,17,-18,18,-18,19,-19,19,-20,20,-20,21,-21,21,-22,22,-22,23,-23,23,-24,24,-24,25,-25,25,-26,26,-26
%N Expansion of g.f. 1/(1 + x + x^3 + x^4).
%C Diagonal sums of Riordan array (1/(1+x+x^2+x^3+x^4),x/(1+x+x^2+x^3+x^4)).
%C Convolution of (n+1)(-1)^n and A010892.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,-1,-1).
%F a(n) = floor((n + 3)/3)*(-1)^n.
%F a(n) = Sum_{k=0..n} ((n - k + 1)(-1)^(n-k)*2sin(Pi*k/3 + Pi/3)/sqrt(3)).
%F G.f.: 1/((1 + x)^2*(1 - x + x^2)).
%F E.g.f.: exp(-x)*(6 - 3*x + exp(3*x/2)*(3*cos(sqrt(3)*x/2) - sqrt(3)*sin(sqrt(3)*x/2)))/9. - _Stefano Spezia_, Feb 12 2023
%F Sum_{n>=0} 1/a(n) = log(2). - _Amiram Eldar_, Feb 14 2023
%t CoefficientList[ Series[1/(1 + x + x^3 + x^4), {x, 0, 80}], x] (* _Robert G. Wilson v_, Mar 24 2005 *)
%t LinearRecurrence[{-1,0,-1,-1},{1,-1,1,-2},90] (* _Harvey P. Dale_, Jan 18 2019 *)
%Y Cf. A008620, A010892.
%K easy,sign
%O 0,4
%A _Paul Barry_, Mar 16 2005
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