A171067 Expansion of g.f. x*(1 - x)*(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, 28421833288321, 106046195130721, 395836628536810

Offset

0,4

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).

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A001739 A072805 A119033 * A121807 A133163 A242831

Adjacent sequences: A171064 A171065 A171066 * A171068 A171069 A171070

Keyword

nonn,easy

Author

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

Status

approved