A108368 Coefficients of x/(1-3*x-3*x^2-x^3).

0, 1, 3, 12, 46, 177, 681, 2620, 10080, 38781, 149203, 574032, 2208486, 8496757, 32689761, 125768040, 483870160, 1861604361, 7162191603, 27555258052, 106013953326, 407869825737, 1569206595241, 6037243216260, 23227219260240, 89362594024741, 343806683071203

Offset

0,3

References

L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 562.

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (3,3,1).

Formula

x=a(n), z=a(-n), y=a(n)+a(n-1), t=a(-n)+a(-n-1) is a solution to 2(x^3+z^3)=y^3+t^3.

G.f.: x/(1-3*x-3*x^2-x^3). a(n)=3a(n-1)+3a(n-2)+a(n-3). a(-1-n)=A108369(n).

Mathematica

CoefficientList[Series[x/(1-3*x-3*x^2-x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{3, 3, 1}, {0, 1, 3}, 40] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2012 *)

Prog

(PARI) a(n)=if(n>=0, polcoeff(x/(1-3*x-3*x^2-x^3)+x*O(x^n), n), n=-1-n; polcoeff(x/(1+3*x+3*x^2-x^3)+x*O(x^n), n))

Crossrefs

Sequence in context: A008781 A047013 A370478 * A264514 A344684 A216946

Adjacent sequences: A108365 A108366 A108367 * A108369 A108370 A108371

Keyword

nonn,easy

Author

Michael Somos, Jun 01 2005

Status

approved