A171066 G.f. -x*(x-1)*(1+x)/(1-x-9*x^2-x^3+x^4).

0, 1, 1, 9, 19, 100, 279, 1189, 3781, 14661, 49600, 184141, 641421, 2333629, 8240959, 29700900, 105561739, 378777169, 1350292761, 4835148121, 17260998400, 61748847081, 220582688041, 788748162049, 2818480203099, 10076047502500

Offset: 0

Author

R. J. Mathar, at the request of R. K. Guy, Sep 03 2010

Keywords

• nonn
• easy

Comments

The member k=9 of a family of sequences starting 0,1,1,k with recurrence a(n) = a(n-1)+k*a(n-2)+a(n-3)-a(n-4).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Hugh Williams, R. K. Guy, Some fourth-order linear divisibility sequences, Intl. J. Number Theory vol. 7 (5) (2011) 1255-1277
• Index entries for linear recurrences with constant coefficients, signature (1,9,1,-1).

Crossrefs

Cf. A116201 (k=1), A105309 (k=2), A152090 (k=3), A007598 (k=4), A005178 (k=5), A003757 (k=6).

Programs

Magma

I:=[0, 1, 1, 9]; [n le 4 select I[n] else Self(n-1) + 9*Self(n-2) + Self(n-3) - Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 19 2012

Mathematica

CoefficientList[Series[-x*(x - 1)*(1 + x)/(1 - x - 9*x^2 - x^3 + x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 19 2012 *)

Formula

a(n)= +a(n-1) +9*a(n-2) +a(n-3) -a(n-4)