OFFSET
0,5
COMMENTS
Sequence is related to rhombus substitution tilings. For the tridiagonal unit-primitive matrix U_1= (0 1 0 0)
(1 0 1 0)
(0 1 0 1)
(0 0 1 1),
let M=(m_(i,j))=(U_1)^n, i,j=1,2,3,4. Then a(n) = m_(2,4).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..3651
Genki Shibukawa, New identities for some symmetric polynomials and their applications, arXiv:1907.00334 [math.CA], 2019.
Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-1).
FORMULA
a(n)=a(n-1)+3*a(n-2)-2*a(n-3)-a(n-4), for n>=4, with {a(k)}={0,0,1,1}, k=0,1,2,3.
a(n)=A187498(3*n).
G.f.: x^2/(1 - x - 3*x^2 + 2*x^3 + x^4) -Michael De Vlieger, Aug 21 2019
MATHEMATICA
LinearRecurrence[{1, 3, -2, -1}, {0, 0, 1, 1}, 40] (* Harvey P. Dale, Jan 26 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
L. Edson Jeffery, Mar 18 2011
STATUS
approved