A218136 Norm of coefficients in the expansion of 1 / (1 - 3*x + 2*I*x^2), where I^2=-1.

1, 9, 85, 873, 8845, 89505, 906373, 9177849, 92932285, 941010705, 9528455221, 96482899305, 976963204333, 9892500250113, 100169136977125, 1014289183762137, 10270454347410973, 103996211523970545, 1053041242918825621, 10662848608027795785, 107969503760905131085

Offset

0,2

Comments

The radius of convergence of g.f. equals (9+sqrt(145) - 3*sqrt(2)*sqrt(9+sqrt(145)))/16 = 0.0987579662...

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (9, 8, 36, -16).

Formula

G.f.: (1-4*x^2) / (1 - 9*x - 8*x^2 - 36*x^3 + 16*x^4).

Example

G.f.: A(x) = 1 + 9*x + 85*x^2 + 873*x^3 + 8845*x^4 + 89505*x^5 + 906373*x^6 +...
The terms equal the norm of the complex coefficients in the expansion:
1/(1-3*x+2*I*x^2) = 1 + 3*x + (9 - 2*I)*x^2 + (27 - 12*I)*x^3 + (77 - 54*I)*x^4 + (207 - 216*I)*x^5 + (513 - 802*I)*x^6 + (1107 - 2820*I)*x^7 +...
so that
a(1) = 3^2, a(2) = 9^2 + 2^2, a(3) = 27^2 + 12^2, a(4) = 77^2 + 54^2, a(5) = 207^2 + 216^2, ...

Mathematica

CoefficientList[Series[(1-4x^2)/(1-9x-8x^2-36x^3+16x^4), {x, 0, 20}], x] (* or *) LinearRecurrence[{9, 8, 36, -16}, {1, 9, 85, 873}, 30] (* Harvey P. Dale, Mar 22 2023 *)

Prog

(PARI) {a(n)=norm(polcoeff(1/(1-3*x+2*I*x^2+x*O(x^n)), n))}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A105309, A218134, A218135.

Sequence in context: A108427 A152106 A142982 * A196955 A361283 A029711

Adjacent sequences: A218133 A218134 A218135 * A218137 A218138 A218139

Keyword

nonn

Author

Paul D. Hanna, Oct 21 2012

Status

approved