OFFSET
0,3
COMMENTS
The coefficients of the recursion for a(n) are given by the 4th row of A145152.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,0,-3,3,-1).
FORMULA
a(n) = 4a(n-1) -6a(n-2) +4a(n-3) -3a(n-5) +3a(n-6) -a(n-7).
EXAMPLE
a(8) = 155 = 4*99 -6*61 +4*36 -3*10 +3*4 -1.
MAPLE
col:= proc(k) local l, j, M, n; l:= `if`(k=0, [1, 0, 0, 1], [seq(coeff( -(1-x-x^4) *(1-x)^(k-1), x, j), j=1..k+3)]); M:= Matrix(nops(l), (i, j)-> if i=j-1 then 1 elif j=1 then l[i] else 0 fi); `if`(k=0, n->(M^n)[2, 3], n->(M^n)[1, 2]) end: a:= col(4): seq(a(n), n=0..40);
MATHEMATICA
CoefficientList[Series[x / ((1 - x - x^4) (1 - x)^3), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)
LinearRecurrence[{4, -6, 4, 0, -3, 3, -1}, {0, 1, 4, 10, 20, 36, 61}, 40] (* Harvey P. Dale, Apr 04 2014 *)
PROG
(PARI) concat(0, Vec(1/(1-x-x^4)/(1-x)^3+O(x^99))) \\ Charles R Greathouse IV, Sep 25 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Oct 03 2008
STATUS
approved