A328605 Expansion of (1 + 5*x - 2*x^2 - 15*x^3) / (1 - 12*x^2 + 25*x^4).

1, 5, 10, 45, 95, 415, 890, 3855, 8305, 35885, 77410, 334245, 721295, 3113815, 6720290, 29009655, 62611105, 270270485, 583326010, 2518004445, 5434634495, 23459291215, 50632463690, 218561383455, 471723701905, 2036254321085, 4394872830610, 18971017266645, 40945381419695

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,12,0,-25).

Formula

a(n) = 12*a(n-2) - 25*a(n-4) for n>3. - Colin Barker, Oct 21 2019

a(2*n)/a(2*n-1) ~ 2*a(2*n+1)/a(2*n) ~ 1 + sqrt(11).

Mathematica

CoefficientList[Series[(1+5x-2x^2-15x^3)/(1-12x^2+25x^4), {x, 0, 30}], x] (* or *) LinearRecurrence[ {0, 12, 0, -25}, {1, 5, 10, 45}, 30] (* Harvey P. Dale, Jul 02 2024 *)

Prog

(PARI) Vec((1 + 5*x - 2*x^2 - 15*x^3) / (1 - 12*x^2 + 25*x^4) + O(x^30)) \\ Colin Barker, Dec 13 2019

Crossrefs

Cf. A328604, A328606.

Sequence in context: A305246 A316546 A187877 * A122173 A083515 A343467

Adjacent sequences: A328602 A328603 A328604 * A328606 A328607 A328608

Keyword

nonn,less,easy

Author

Kyle MacLean Smith, Oct 20 2019

Status

approved