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A089074 Let m0 be the matrix {{0,1,0,0},{0,0,1,0},{0,0,0,1},{1,1,1,1}}; a(n) = Floor[Re[MatrixPower[m0,n][[4,4]]]] 0
0, 1, 3, 7, 14, 28, 55, 107, 207, 400, 772, 1489, 2871, 5535, 10670, 20568, 39647, 76423, 147311, 283952, 547336, 1055025, 2033627, 3919943, 7555934, 14564532, 28074039, 54114451, 104308959, 201061984, 387559436, 747044833, 1439975215 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..33.

Index entries for linear recurrences with constant coefficients, signature (2,0,0,0,-1).

FORMULA

G.f.: x*(1+x+x^2)/(1-2*x+x^5). a(n) = 2*a(n-1) - a(n-5) for n >= 6. - N. J. A. Sloane, Dec 05, 2003

MATHEMATICA

digits=100 NSolve[x^4-x^3-x^2-x-1==0, x] k=1.9275619754829254 q=k^2-k-1/k-1/k^2 m0={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 1, 1, q}} m[n_]=MatrixPower[m0, n] a=Table[Floor[Re[m[n][[4, 4]]]], {n, 1, digits}]

CROSSREFS

Equals A000078(n+3) + 1.

Sequence in context: A285447 A140741 A088209 * A125176 A153234 A293334

Adjacent sequences:  A089071 A089072 A089073 * A089075 A089076 A089077

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Dec 04 2003

STATUS

approved

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Last modified August 9 04:39 EDT 2020. Contains 336319 sequences. (Running on oeis4.)