A338186 Expansion of (2-6*x-12*x^2)/((1-x)^2*(1-9*x)).

2, 16, 126, 1100, 9850, 88584, 797174, 7174468, 64570098, 581130752, 5230176622, 47071589436, 423644304746, 3812798742520, 34315188682470, 308836698142004, 2779530283277794, 25015772549499888, 225141952945498718, 2026277576509488172, 18236498188585393242, 164128483697268538856

Offset: 0

Author

Georg Fischer, Oct 15 2020

Keywords

• nonn
• easy

Comments

The locally small terms 4^k in A322469 occur at the positions a(k) (for k = 0..9, and probably in general; cf. conjectures in A322469).

Examples

			A322469(a(4)) = A322469(9850) = 256 = 4^4.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (11,-19,9).

Crossrefs

Cf. A322469.

Programs

Maple

f:= gfun:-rectoproc({a(n)=11*a(n-1)-19*a(n-2)+9*a(n-3), a(0)=2, a(1)=16, a(2)=126}, a(n), remember): map(f, [$0..21]);

Mathematica

CoefficientList[Series[(2-6*x-12*x^2)/((1-x)^2*(1-9*x)), {x,0,21}], x]

PARI

my(x='x+O('x^22)); Vec((2-6*x-12*x^2)/((1-x)^2*(1-9*x)))

Formula

a(n) = 11*a(n-1) - 19*a(n-2) + 9*a(n-3) for n >= 3.