A202012 - OEIS

%I #32 Jun 30 2026 22:37:20

%S 1,1,3,6,11,21,39,72,133,245,451,830,1527,2809,5167,9504,17481,32153,

%T 59139,108774,200067,367981,676823,1244872,2289677,4211373,7745923,

%U 14246974,26204271,48197169,88648415,163049856

%N Expansion of (1-x+x^2)/((1-x)(1-x-x^2-x^3)).

%C Antidiagonal sums of triangle T(n,k) = A104040(n,k)*(-1)^floor(k/2). - _Philippe Deléham_, Dec 11 2011

%H Harvey P. Dale, <a href="/A202012/b202012.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,-1).

%F a(n) = 2*a(n-1) - a(n-4), n>3.

%F a(n) = A008937(n-1) - A008937(n) + A008937(n+1). - _R. J. Mathar_, Dec 10 2011

%F a(n+1)-a(n) = A081172(n+2). - _Philippe Deléham_, Dec 11 2011

%t CoefficientList[Series[(1-x+x^2)/((1-x)(1-x-x^2-x^3)),{x,0,40}],x] (* _Harvey P. Dale_, Apr 21 2014 *)

%t (* Alternative: *)

%t LinearRecurrence[{2,0,0,-1},{1,1,3,6},40] (* _Harvey P. Dale_, Apr 21 2014 *)

%Y Cf. A008937, A081172, A104040.

%K easy,nonn

%O 0,3

%A _Philippe Deléham_, Dec 08 2011