A171067 G.f. -x*(x-1)*(1+x)/((x^2+3*x+1)*(x^2-4*x+1)).

0, 1, 1, 10, 21, 121, 340, 1561, 5061, 20890, 72721, 285121, 1028160, 3931201, 14425201, 54480250, 201635301, 756931801, 2813339860, 10529812921, 39218508021, 146573045290, 546474598561, 2040893746561, 7612994269440

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

The member k=10 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 (1,10,1,-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, 10]; [n le 4 select I[n] else Self(n-1) + 10*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)/((x^2 + 3*x + 1)*(x^2 - 4*x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 19 2012 *)
LinearRecurrence[{1,10,1,-1},{0,1,1,10},30] (* Harvey P. Dale, Dec 24 2017 *)

Formula

a(n)= +a(n-1) +10*a(n-2) +a(n-3) -a(n-4).

a(n)= -(-1)^n*A005248(n)/7 + 2*A001075(n)/7.