A083839 G.f.: ( x - 3*x^2 + 6*x^3 - 8*x^4 + 4*x^5 - x^7 ) / (1 - 4*x + 6*x^2 - 5*x^3 + 2*x^4 + x^5 - x^6 + x^7 ).

0, 1, 1, 4, 7, 11, 19, 36, 67, 121, 216, 386, 691, 1236, 2206, 3929, 6987, 12411, 22024, 39046, 69162, 122406, 216481, 382606, 675811, 1193061, 2105156, 3712864, 6545672, 11535476, 20322024, 35789966, 63012987, 110913356, 195178616, 343387111, 604014136

Offset

0,4

References

O. Martin, A. M. Odlyzko and S. Wolfram, Algebraic properties of cellular automata, Comm. Math. Physics, 93 (1984), pp. 219-258, Reprinted in Theory and Applications of Cellular Automata, S. Wolfram, Ed., World Scientific, 1986, pp. 51-90 and in Cellular Automata and Complexity: Collected Papers of Stephen Wolfram, Addison-Wesley, 1994, pp. 71-113. See Eq. 5.7.

Links

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (4,-6,5,-2,-1,1,-1).

Formula

G.f.: x*( 1-3*x-8*x^3+4*x^4-x^6+6*x^2 ) / ( (x^2-x+1)*(x^2+x-1)*(x^3-x^2+2*x-1) ). - R. J. Mathar, Sep 27 2014

Mathematica

CoefficientList[Series[(x-3x^2+6x^3-8x^4+4x^5-x^7)/(1-4x+6x^2-5x^3+2x^4+x^5-x^6+x^7), {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 5, -2, -1, 1, -1}, {0, 1, 1, 4, 7, 11, 19, 36}, 50] (* Harvey P. Dale, Jun 09 2019 *)

Crossrefs

Sequence in context: A310768 A109328 A228079 * A091176 A002974 A130625

Adjacent sequences: A083836 A083837 A083838 * A083840 A083841 A083842

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 19 2003

Status

approved