|
|
A224232
|
|
a(n) = n! if n <= 3, otherwise a(n) = 2*(a(n-1) + a(n-3)) + a(n-2).
|
|
6
|
|
|
1, 1, 2, 6, 16, 42, 112, 298, 792, 2106, 5600, 14890, 39592, 105274, 279920, 744298, 1979064, 5262266, 13992192, 37204778, 98926280, 263041722, 699419280, 1859732842, 4944968408, 13148508218, 34961450528, 92961346090, 247181159144, 657246565434, 1747596982192, 4646802848106, 12355695809272, 32853388431034, 87356078367552, 232276936784682
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Also the number of permutations that are sortable after two passes through a pop stack. (See the Pudwell-Smith link.) - Lara Pudwell, Jun 01 2017
|
|
LINKS
|
Lara Pudwell and Rebecca Smith, Sorting with Pop Stacks, Special Session on Algebraic and Enumerative Combinatorics with Applications, AMS Central Section Spring Meeting, 2017.
|
|
FORMULA
|
G.f.: (x^3 + x^2 + x - 1) / (2*x^3 + x^2 + 2*x - 1). - Colin Barker, Jun 07 2015
|
|
MATHEMATICA
|
CoefficientList[Series[(x^3 + x^2 + x - 1)/(2 x^3 + x^2 + 2 x - 1), {x, 0, 35}], x] (* Michael De Vlieger, Jun 01 2017 *)
LinearRecurrence[{2, 1, 2}, {1, 1, 2, 6}, 40] (* Harvey P. Dale, Aug 28 2023 *)
|
|
PROG
|
(PARI) Vec((x^3+x^2+x-1)/(2*x^3+x^2+2*x-1) + O(x^100)) \\ Colin Barker, Jun 07 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|