

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(n1) 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^22*x1)*x / (2*x^3+x^2+3*x1).
Recurrence: a(n) = 3*a(n1) + a(n2)  2*a(n3).
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



