OFFSET
0,1
COMMENTS
This sequence is eventually polynomial.
REFERENCES
N. Shar, Experimental methods in permutation patterns and bijective proof, PhD thesis, Rutgers University (2016)
FORMULA
For n >= 2, a(n) = (32/3)*n^6 + 32*n^5 + (80/3)*n^4 + (16/3)*n^3 + 38/3*n^2 + 59/3*n + 13 (conjectured).
Conjectures from Colin Barker, Apr 11 2016: (Start)
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7) for n>6.
G.f.: (6+77*x+1572*x^2+4378*x^3+1531*x^4+137*x^5-22*x^6+x^8) / (1-x)^7.
(End)
Remark by Nathaniel Shar, Apr 13 2016: The preceding three conjectures are equivalent (provided appropriate initial conditions are specified for the recurrence relation).
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Nathaniel Shar, Apr 11 2016
STATUS
approved