A339252 a(0) = 1, a(1) = 4, a(2) = 11, and a(n) = 4*a(n-1) - 4*a(n-2) for n >= 3.

1, 4, 11, 28, 68, 160, 368, 832, 1856, 4096, 8960, 19456, 41984, 90112, 192512, 409600, 868352, 1835008, 3866624, 8126464, 17039360, 35651584, 74448896, 155189248, 322961408, 671088640, 1392508928, 2885681152, 5972688896, 12348030976, 25501368320, 52613349376

Offset: 0

Author

Peter Kagey and Peter Luschny, Nov 28 2020

Keywords

• nonn
• easy

Links

• Peter Kagey, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4).

Crossrefs

Cf. A207615, A106472 (quarter).

Programs

Maple

a := proc(n) option remember; if n <= 2 then return [1, 4, 11][n+1] fi;
4*a(n - 1) - 4*a(n - 2) end: seq(a(n), n = 0..31);

Mathematica

CoefficientList[Series[(1 - x^2)/(1 - 2*x)^2, {x, 0, 50}], x]

Formula

G.f.: (1 - x^2)/(1 - 2*x)^2.

a(n) = A207615(n+2, 2).

a(n) = 2^(n-2)*(3*n + 5) for n >= 1. - Kevin Ryde, Nov 28 2020

E.g.f.: (exp(2*x)*(5 + 6*x) - 1)/4. - Stefano Spezia, May 14 2023