OFFSET
0,4
COMMENTS
Bob Hanlon (hanlonr(AT)cox.net) helped convert the expansion to a recursion.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (-4*x^8-6*x^7-9*x^6-4*x^5-5*x^4-6*x^3-x^2-x-1) / (64*x^12 +69*x^9 +21*x^6 -x^3-1).
MAPLE
a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <64|69|21|-1>>^ iquo(n, 3, 'r'). `if`(r=0, <<1, 5, 25, 149>>, `if`(r=1, <<1, 4, 23, 130>>, <<1, 3, 22, 110>>)))[1, 1]: seq (a(n), n=0..40); # Alois P. Heinz, Feb 11 2012
MATHEMATICA
(* expansion*)
Table[8^(1 + Floor[n/3])*SeriesCoefficient[Series[1/(8 - 8 x + 3 x^3 - 2 x^4), {x, 0, 50}], n], {n, 0, 50}]
(*recursion*)
a[1] = 1; a[2] = 1; a[3] = 1; a[4] = 5; a[5] = 4; a[6] = 3;
a[7] = 25; a[8] = 23; a[9] = 22; a[10] = 149; a[11] = 130;
a[12] = 110;
a[n_Integer?Positive] := a[n] = 64*a[-12 + n] + 69*a[-9 + n] + 21*a[-6 +n] - a[-3 + n]
Table[a[n], {n, 1, 50}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Feb 09 2012
STATUS
approved