A099269 A sequence derived from a matrix using "0,1,2,3,4,5,6".

1, 4, 32, 222, 1610, 11582, 83518, 601974, 4339414, 31280470, 225485414, 1625410326, 11716765478, 84460262198, 608831511430

Offset

1,2

Comments

Recursion multipliers are seen in rightmost coefficients of the matrix characteristic polynomial, with changed signs: x^3 - 7x^2 - 4x + 18. a(n)/a(n-1) tends to 7.2084965573...a root of the polynomial and an eigenvalue of the matrix.

Links

Table of n, a(n) for n=1..15.

Index entries for linear recurrences with constant coefficients, signature (7,4,-18).

Formula

Let M = the 3 X 3 matrix [4 5 6 / 2 3 0 / 1 0 0]. a(n) = rightmost term in M^n * [1 0 0]. a(n+3) = 7*a(n+2) + 4*a(n+1) - 18*a(n).

G.f.: -x*(3*x-1) / (18*x^3-4*x^2-7*x+1). [Colin Barker, Dec 06 2012]

Example

a(5) = 1610 since M^5 * [1 0 0] = [11582 5506 1610]
a(9) = 4339414 = 7*601974 + 4*83518 - 18*11582 = 7*a(8) + 4*a(7) - 18*a(6).

Crossrefs

Sequence in context: A298965 A316955 A299735 * A316810 A299656 A125823

Adjacent sequences: A099266 A099267 A099268 * A099270 A099271 A099272

Keyword

nonn,easy

Author

Gary W. Adamson, Oct 10 2004

Status

approved