OFFSET
0,6
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
M. H. Albert, M. D. Atkinson and Robert Brignall, The enumeration of three pattern classes, arXiv:1206.3183 [math.CO], 2012.
Index entries for linear recurrences with constant coefficients, signature (4,-2,-7,4,4).
FORMULA
G.f.: x^4*(1-2*x+x^4)/((1+x)*(1-2*x)^2*(1-x-x^2)) (half of A219752).
a(n) = (2^(n-5)*(3*n+16)+4*(-1)^n)/9+((1-sqrt(5))^(n-3)-(1+sqrt(5))^(n-3))/(2^(n-3)*sqrt(5)) with n>3, a(0)=a(1)=a(2)=a(3)=0. [Bruno Berselli, Nov 29 2012]
MAPLE
A219753 := proc(n)
if n < 4 then
0 ;
else
128*(-1)^n+2^n*(16+3*n)-288*A000045(n-3) ;
%/288 ;
end if ;
end proc:
seq(A219753(n), n=0..20) ; # R. J. Mathar, Aug 19 2022
MATHEMATICA
CoefficientList[Series[x^4 (1 - 2 x + x^4)/((1 + x) (1 - 2 x)^2 (1 - x - x^2)), {x, 0, 35}], x] (* Bruno Berselli, Nov 30 2012 *)
LinearRecurrence[{4, -2, -7, 4, 4}, {0, 0, 0, 0, 1, 2, 6, 13, 31}, 40] (* Harvey P. Dale, Oct 05 2021 *)
PROG
(Maxima) makelist(coeff(taylor(x^4*(1-2*x+x^4)/((1+x)*(1-2*x)^2*(1-x-x^2)), x, 0, n), x, n), n, 0, 35); /* Bruno Berselli, Nov 29 2012 */
(Magma) I:=[0, 0, 0, 0, 1, 2, 6, 13, 31]; [n le 9 select I[n] else 4*Self(n-1) - 2*Self(n-2) - 7*Self(n-3) + 4*Self(n-4) + 4*Self(n-5): n in [1..40]]; // Vincenzo Librandi, Dec 14 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 28 2012
STATUS
approved