A051111 Expansion of x/(x^4-3*x^3+4*x^2-2*x+1).

0, 1, 2, 0, -5, -5, 8, 21, 0, -55, -55, 89, 233, 0, -610, -610, 987, 2584, 0, -6765, -6765, 10946, 28657, 0, -75025, -75025, 121393, 317811, 0, -832040, -832040, 1346269, 3524578, 0, -9227465, -9227465, 14930352, 39088169, 0, -102334155, -102334155

Offset

1,3

Links

Table of n, a(n) for n=1..41.

Index entries for two-way infinite sequences

Index entries for linear recurrences with constant coefficients, signature (2,-4,3,-1).

Formula

a(5*n + 1) = F(5*n + 1), a(5*n + 2) = F(5*n + 3), a(5*n + 3) = 0, a(5*n - 1) = a(5*n) = -F(5*n), where F = A000045 the Fibonacci sequence.

G.f.: x / (x^4 - 3*x^3 + 4*x^2 - 2*x + 1). - Michael Somos, Apr 25 2003

Example

x + 2*x^2 - 5*x^4 - 5*x^5 + 8*x^6 + 21*x^7 - 55*x^9 - 55*x^10 + 89*x^11 + ...

Mathematica

CoefficientList[Series[x/(x^4-3x^3+4x^2-2x+1), {x, 0, 40}], x] (* or *) LinearRecurrence[{2, -4, 3, -1}, {0, 1, 2, 0}, 50] (* Harvey P. Dale, Aug 09 2020 *)

Prog

(PARI) {a(n) = local(x, y); x = fibonacci(n); y = fibonacci(n+1); [ -x, x, y, 0, -y][n%5 + 1]}

Crossrefs

Cf. A000045.

Sequence in context: A361582 A137421 A155524 * A068558 A245058 A240657

Adjacent sequences: A051108 A051109 A051110 * A051112 A051113 A051114

Keyword

sign

Author

Michael Somos, Oct 07 1999

Extensions

Zero prepended by Harvey P. Dale, Aug 09 2020

Status

approved