A054147 a(n) = T(2n,n), array T as in A054144.

0, 3, 21, 108, 492, 2100, 8604, 34272, 133728, 513648, 1948560, 7318080, 27256896, 100815936, 370684608, 1355996160, 4938304512, 17914202880, 64760732928, 233390693376, 838784916480, 3006980379648, 10755352869888

Offset: 0

Author

Clark Kimberling, Mar 18 2000

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-20,16,-4).

Crossrefs

Cf. A054144.

Programs

GAP

a:=[0,3,21,108];; for n in [5..30] do a[n]:=8*a[n-1]-20*a[n-2] +16*a[n-3]-4*a[n-4]; od; a; # G. C. Greubel, Jul 31 2019

Magma

R:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( 3*x*(1-x)/(1-4*x+2*x^2)^2 )); // G. C. Greubel, Jul 31 2019

Mathematica

LinearRecurrence[{8,-20,16,-4}, {0,3,21,108}, 30] (* G. C. Greubel, Jul 31 2019 *)

PARI

my(x='x+O('x^30)); concat([0], Vec(3*x*(1-x)/(1-4*x+2*x^2)^2)) \\ G. C. Greubel, Jul 31 2019

Sage

(3*x*(1-x)/(1-4*x+2*x^2)^2).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jul 31 2019

Formula

G.f.: 3*x*(1-x)/(1-4*x+2*x^2)^2.

From Colin Barker, Aug 01 2019: (Start)

a(n) = 8*a(n-1) - 20*a(n-2) + 16*a(n-3) - 4*a(n-4) for n>3.

a(n) = 3*((-(2-sqrt(2))^n*(-1+sqrt(2)) + (1+sqrt(2))*(2+sqrt(2))^n)*n) / 8.

(End)