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A100297 Sequence generated from a symmetric matrix composed of Catalan numbers. 0
1, 6, 89, 1430, 23070, 372259, 6006853, 96927945, 1564051382, 25237889117, 407244323586, 6571387104706, 106037398138915, 1711043593219257, 27609788897887265, 445517838357152822, 7188977251094395521, 116002973320502471614, 1871850382771577632966 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n)/a(n-1) tends to 16.136227625...an eigenvalue of M and a root of the characteristic polynomial x^3 - 17x^2 + 14x - 1.

LINKS

Table of n, a(n) for n=1..19.

Index entries for linear recurrences with constant coefficients, signature (17,-14,1).

FORMULA

a(n) = leftmost term in M^n * [1 0 0], where M = the 3 X 3 matrix [1 1 2 / 1 2 5 / 2 5 14]. a(n) = 17*a(n-1) - 14*a(n-2) + a(n-3).

G.f.: -x*(x^2-11*x+1) / (x^3-14*x^2+17*x-1). [Colin Barker, Dec 13 2012]

EXAMPLE

a(4) = 1430 since M^4 * [1 0 0] = [1430 3338 9151].

a(6) = 372259 = 17*23070 - 14*1430 + 89 = 17*a(5) - 14*a(4) + a(3).

CROSSREFS

Sequence in context: A127183 A054952 A101148 * A177568 A177573 A166782

Adjacent sequences:  A100294 A100295 A100296 * A100298 A100299 A100300

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Nov 11 2004

EXTENSIONS

More terms from Colin Barker, Dec 13 2012

STATUS

approved

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Last modified October 22 10:39 EDT 2021. Contains 348160 sequences. (Running on oeis4.)