A168639 Expansion of x*(1 + x^2 - x^3) / ( (1-x)*(1-x-x^4) ).

0, 1, 2, 4, 5, 7, 10, 15, 21, 29, 40, 56, 78, 108, 149, 206, 285, 394, 544, 751, 1037, 1432, 1977, 2729, 3767, 5200, 7178, 9908, 13676, 18877, 26056, 35965, 49642, 68520, 94577, 130543, 180186, 248707, 343285, 473829, 654016, 902724, 1246010, 1719840, 2373857, 3276582

Offset

0,3

Comments

Limiting ratio is: 1.38028, see A086106.

References

R. Pallu de la Barriere, Optimal Control Theory,Dover Publications, New York,1967,pages 339-344

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n)= 2*a(n-1) -a(n-2) +a(n-4) -a(n-5). - R. J. Mathar, Dec 02 2009

a(n) = A098578(n) - A098578(n-3) + A098578(n-2). - R. J. Mathar, May 23 2013

Mathematica

Clear[n, m, v, M, a, b, c, K]
M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 1}}
v[0] = {0, 0, 0, 1};
v[n_] := v[n] = M.v[n - 1] + {1, 1, 1, 1}
a = Table[v[n][[1]], {n, 0, 30}]
LinearRecurrence[{2, -1, 0, 1, -1}, {0, 1, 2, 4, 5}, 50] (* G. C. Greubel, Jul 28 2016 *)

Prog

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; -1, 1, 0, -1, 2]^n*[0; 1; 2; 4; 5])[1, 1] \\ Charles R Greathouse IV, Jul 29 2016

Crossrefs

Cf. A098578.

Sequence in context: A241735 A092295 A277102 * A275802 A218931 A331518

Adjacent sequences: A168636 A168637 A168638 * A168640 A168641 A168642

Keyword

nonn,easy

Author

Roger L. Bagula and Gary W. Adamson, Dec 01 2009

Status

approved