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A100296 Sequence generated from a symmetric matrix. 1
1, 6, 25, 111, 488, 2149, 9461, 41654, 183389, 807403, 3554736, 15650361, 68903513, 303360038, 1335596817, 5880203831, 25888648920, 113979406525, 501814720109, 2209329044566, 9726966211957, 42824708216851, 188543436246752, 830096195208753, 3654646945111665 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A100295 is generated from M^n * [1 0 0]. a(n)/a(n-1) tends to 4.4026788295...a root of the characteristic polynomial of M, x^3 - 4x^2 - 2x + 1 and an eigenvalue of M.

LINKS

Table of n, a(n) for n=1..25.

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

FORMULA

a(n) = rightmost term in M^n * [1 1 1]. a(n) = 4*a(n-1) + 2*a(n-2) - a(n-3).

G.f.: -x*(x^2-2*x-1) / (x^3-2*x^2-4*x+1). - Colin Barker, May 25 2013

EXAMPLE

a(5) = 488 since M^5 * [1 1 1] = [2149 1263 488]. 2149 = a(6).

a(8) = 4*a(7) + 2*a(6) - a(5) =41654 = 4*9461 + 2*2149 - 488.

CROSSREFS

Cf. A100295.

Sequence in context: A295202 A346894 A094669 * A346818 A120758 A227914

Adjacent sequences:  A100293 A100294 A100295 * A100297 A100298 A100299

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Nov 11 2004

EXTENSIONS

More terms from Colin Barker, May 25 2013

STATUS

approved

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Last modified September 26 13:34 EDT 2021. Contains 347668 sequences. (Running on oeis4.)