A383740 a(0) = 4; a(n) = Pell(4*n)/Pell(n) for n > 0.

4, 12, 204, 2772, 39236, 551532, 7761996, 109216308, 1536797956, 21624369228, 304278011724, 4281516425748, 60245508232004, 847718631046572, 11928306344398284, 167844007448966772, 2361744410638758916, 33232265756370284172, 467613464999874177996, 6579820775754484587348

Offset

0,1

Links

Harvey P. Dale, Table of n, a(n) for n = 0..870

Index entries for linear recurrences with constant coefficients, signature (12,30,-12,-1).

Formula

a(n) = 12*a(n-1) + 30*a(n-2) - 12*a(n-3) - a(n-4).

G.f.: 4 * (1-9*x-15*x^2+3*x^3)/((1+2*x-x^2) * (1-14*x-x^2)).

Mathematica

a[n_] := Fibonacci[4*n, 2]/Fibonacci[n, 2]; a[0] = 4; Array[a, 20, 0] (* Amiram Eldar, May 08 2025 *)
LinearRecurrence[{12, 30, -12, -1}, {4, 12, 204, 2772}, 30] (* Harvey P. Dale, Jan 17 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(4*(1-9*x-15*x^2+3*x^3)/((1+2*x-x^2)*(1-14*x-x^2)))

Crossrefs

Row n=4 of A383742.

Cf. A000129, A099930.

Sequence in context: A213143 A173603 A175718 * A076030 A383664 A348789

Adjacent sequences: A383737 A383738 A383739 * A383741 A383742 A383743

Keyword

nonn,easy

Author

Seiichi Manyama, May 07 2025

Status

approved