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A216271 Expansion of (1-x)/((1-2x)(1-4x+x^2)). 1

%I #14 Feb 01 2020 19:04:21

%S 1,5,21,83,319,1209,4549,17051,63783,238337,890077,3322995,12403951,

%T 46296905,172791861,644886923,2406788599,8982333009,33522674509,

%U 125108627171,466912358463,1742541855257,6503257159717,24270490977915,90578715140551,338044386361505,1261598863859901

%N Expansion of (1-x)/((1-2x)(1-4x+x^2)).

%C Partial sums are in A216263.

%C Diagonal of square array A214846.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,2).

%F a(n) = A001353(n+2) - A087946(n+1).

%F G.f.: (1-x)/(1-6x+9x^2-2x^3).

%F a(n) = 6*a(n-1) - 9*a(n-2) + 2*a(n-3), a(0) = 1, a(1) = 5, a(2) = 21.

%F Sum_{k=0..n} a(k) = A216263(n).

%t CoefficientList[Series[(1-x)/((1-2x)(1-4x+x^2)),{x,0,30}],x] (* _Harvey P. Dale_, Oct 05 2019 *)

%Y Cf. A001353, A087946, A214846, A216263.

%K nonn,easy

%O 0,2

%A _Philippe Deléham_, Mar 16 2013

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Last modified March 29 08:53 EDT 2024. Contains 371268 sequences. (Running on oeis4.)