A262594 Expansion of (1-2*x)^2/((1-x)^4*(1-4*x)).

1, 4, 14, 52, 203, 808, 3232, 12936, 51765, 207100, 828466, 3313964, 13255999, 53024192, 212097028, 848388448, 3393554217, 13574217396, 54296870230, 217187481700, 868749927731, 3474999712024, 13899998849384, 55599995399032, 222399981597853, 889599926393388, 3558399705575802, 14233598822305756

Offset: 0

Author

N. J. A. Sloane, Oct 22 2015

Keywords

• nonn
• easy

Comments

Suggested by A262592.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-22,28,-17,4).

Crossrefs

Cf. A262592.

Programs

Mathematica

CoefficientList[Series[(1-2x)^2/((1-x)^4(1-4x)),{x,0,40}],x] (* or *) LinearRecurrence[ {8,-22,28,-17,4},{1,4,14,52,203},40] (* Harvey P. Dale, Jul 04 2022 *)

PARI

a(n) = (34+2^(7+2*n)+93*n+18*n^2-9*n^3)/162 \\ Colin Barker, Oct 23 2015

PARI

Vec((1-2*x)^2/((1-x)^4*(1-4*x)) + O(x^40)) \\ Colin Barker, Oct 23 2015

Formula

From Colin Barker, Oct 23 2015: (Start)

a(n) = 8*a(n-1)-22*a(n-2)+28*a(n-3)-17*a(n-4)+4*a(n-5) for n>4.

a(n) = (34+2^(7+2*n)+93*n+18*n^2-9*n^3)/162.

(End)