OFFSET
0,9
REFERENCES
D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: x^7/(x^5 + x^3 - 3*x^2 + 3*x - 1)^2. - Alois P. Heinz, Oct 23 2008
MAPLE
a:= n-> (Matrix(10, (i, j)-> if i=j-1 then 1 elif j=1 then [6, -15, 20, -15, 8, -7, 6, -2, 0, -1][i] else 0 fi)^n)[1, 8]:
seq(a(n), n=0..50); # Alois P. Heinz, Oct 23 2008
MATHEMATICA
t[i_, j_] := If[i == j-1, 1, If[j == 1, {6, -15, 20, -15, 8, -7, 6, -2, 0, -1}[[i]] , 0]]; M = Array[t, {10, 10}]; a[n_] := MatrixPower[M, n][[1, 8]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 13 2015, after Alois P. Heinz *)
PROG
(Magma) [&+[k*Binomial(n-2*k, 3*k+2): k in [0..(n div 2)]]: n in [0..40]]; // Bruno Berselli, Feb 13 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Don Knuth, Apr 11 2008
STATUS
approved