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

1, 5, 21, 83, 319, 1209, 4549, 17051, 63783, 238337, 890077, 3322995, 12403951, 46296905, 172791861, 644886923, 2406788599, 8982333009, 33522674509, 125108627171, 466912358463, 1742541855257, 6503257159717, 24270490977915, 90578715140551, 338044386361505, 1261598863859901

Offset: 0

Author

Philippe Deléham, Mar 16 2013

Keywords

• nonn
• easy

Comments

Partial sums are in A216263.

Diagonal of square array A214846.

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-9,2).

Crossrefs

Cf. A001353, A087946, A214846, A216263.

Programs

Mathematica

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

Formula

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

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

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

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