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A100059 First differences of A052911. 2
1, 5, 14, 45, 139, 434, 1351, 4209, 13110, 40837, 127203, 396226, 1234207, 3844441, 11975078, 37301261, 116189979, 361921042, 1127350583, 3511592833, 10938286998, 34071752661, 106130359315, 330586256610 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n)/a(n-1) tends to 3.11490754148...an eigenvalue of M and a root of the characteristic polynomial x^3 - 3x^2 - x + 2.

REFERENCES

Boris A. Bondarenko, "Generalized Pascal Triangles and Pyramids, Their Fractals, Graphs and Applications"; Fibonacci Association, 1993, p. 27.

LINKS

Table of n, a(n) for n=1..24.

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

FORMULA

G.f.: (2*x^2-2*x-1)*x / (-2*x^3+x^2+3*x-1).

Recurrence: a(n) = 3*a(n-1) + a(n-2) - 2*a(n-3).

a(n) = rightmost term in M^5 * [1 1 1], where M = the 3 X 3 upper triangular matrix [2 1 2 / 1 1 0 / 1 0 0].

INVERT transform of (1, 4, 5, 6, 7, 8, 9,...) with offset 0.

EXAMPLE

a(5) = 139 = rightmost term in M^5 * [1 1 1] which is [434 205 139]. 434 = a(6), while 205 = A052911(5).

a(6) = 434 = 3*a(5) + a(4) - 2*a(3) = 3*139 + 45 - 2*14.

MATHEMATICA

LinearRecurrence[{3, 1, -2}, {1, 5, 14}, 30] (* Harvey P. Dale, Apr 21 2016 *)

CROSSREFS

Cf. A019481, A052550, A052939, A100058, A058071.

Sequence in context: A302762 A140796 A197212 * A270062 A236043 A270661

Adjacent sequences:  A100056 A100057 A100058 * A100060 A100061 A100062

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Oct 31 2004

EXTENSIONS

Edited by Ralf Stephan, Nov 02 2004

STATUS

approved

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Last modified February 22 12:42 EST 2020. Contains 332136 sequences. (Running on oeis4.)