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A188021
Expansion of (x^2)/[(1-x)*(1-3*x^2-x^3)].
2
0, 0, 1, 1, 4, 5, 14, 20, 48, 75, 165, 274, 571, 988, 1988, 3536, 6953, 12597, 24396, 44745, 85786, 158632, 302104, 561683, 1064945, 1987154, 3756519, 7026408, 13256712, 24835744, 46796545, 87763945, 165225380, 310088381, 583440086, 1095490524
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).
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
Sequence in context: A041089 A042321 A050164 * A191790 A246984 A306897
KEYWORD
nonn
AUTHOR
L. Edson Jeffery, Mar 18 2011
STATUS
approved