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A073357 Binomial transform of tribonacci numbers. 4
0, 1, 3, 8, 22, 62, 176, 500, 1420, 4032, 11448, 32504, 92288, 262032, 743984, 2112384, 5997664, 17029088, 48350464, 137280832, 389779648, 1106696192, 3142227840, 8921685888 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For n-> infinity the ratio a(n)/a(n-1) approaches 1+c, where c is the real root of the cubic x^3-x^2-x-1=0; c=1.8392867...

a(n) = rightmost term of M^n *[100] where M = the 3X3 matrix [1 1 0 / 0 1 1 / 1 1 2]. Middle term of the vector = partial sums of A073357 through a(n-1). E.g., M^5*[1 0 0] = [18 34 62] where 62 = a(5) and 34 = partial sums of A073357 through a(4): 34 = 0+1+3+8+22. - Gary W. Adamson, Jul 24 2005

REFERENCES

Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego, CA: Academic Press, 1995.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

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

FORMULA

a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-3), a(0)=0, a(1)=1, a(2)=3.

Generating function A(x)=(x-x^2)/(1-4x+4x^2-2x^3).

a(n) = A115390(n+1) - A115390(n). - R. J. Mathar, Apr 16 2009

MATHEMATICA

h[n_] := h[n]=4*h[n-1]-4*h[n-2]+2*h[n-3]; h[0]=0; h[1]=1; h[2]=3

LinearRecurrence[{4, -4, 2}, {0, 1, 3}, 30] (* Harvey P. Dale, Nov 13 2011 *)

CROSSREFS

Cf. A000073, A073313. Trisection of A103685.

Sequence in context: A027036 A018040 A018041 * A278614 A188464 A298260

Adjacent sequences:  A073354 A073355 A073356 * A073358 A073359 A073360

KEYWORD

easy,nonn

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Jul 29 2002

STATUS

approved

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Last modified July 8 02:24 EDT 2020. Contains 335503 sequences. (Running on oeis4.)