|
|
A254660
|
|
Numbers of words on alphabet {0,1,...,6} with no subwords ii, where i is from {0,1,...,4}.
|
|
5
|
|
|
1, 7, 44, 278, 1756, 11092, 70064, 442568, 2795536, 17658352, 111541184, 704563808, 4450465216, 28111918912, 177572443904, 1121658501248, 7085095895296, 44753892374272, 282693546036224, 1785669060965888, 11279401457867776, 71247746869138432
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1 + x)/(1 - 6*x -2*x^2).
a(n) = 6*a(n-1) + 2*a(n-2) with n>1, a(0) = 1, a(1) = 7.
a(n) = ((3-sqrt(11))^n*(-4+sqrt(11)) + (3+sqrt(11))^n*(4+sqrt(11))) / (2*sqrt(11)). - Colin Barker, Jan 21 2017
|
|
MATHEMATICA
|
RecurrenceTable[{a[0] == 1, a[1] == 7, a[n] == 6 a[n - 1] + 2 a[n - 2]}, a[n], {n, 0, 20}]
|
|
PROG
|
(PARI) Vec((1 + x) / (1 - 6*x -2*x^2) + O(x^30)) \\ Colin Barker, Jan 21 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|