A279558
Number of length n inversion sequences avoiding the patterns 010, 120, and 210.
Original entry on oeis.org
1, 1, 2, 5, 15, 52, 200, 830, 3654, 16869, 80963, 401300, 2043610, 10649335, 56604706, 306101789, 1680515427
Offset: 0
The length 4 inversion sequences avoiding (010, 120, 210) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.
Cf.
A000108,
A263777,
A263778,
A263779,
A263780,
A279551,
A279552,
A279553,
A279554,
A279555,
A279556,
A279557,
A279559,
A279560,
A279561,
A279562,
A279563,
A279564,
A279565,
A279566,
A279567,
A279568,
A279569,
A279570,
A279571,
A279572,
A279573.
A279572
Number of length n inversion sequences avoiding the patterns 120, 201, and 210.
Original entry on oeis.org
1, 1, 2, 6, 23, 101, 484, 2468, 13166, 72630, 411076, 2374188, 13938018, 82932254, 499031324, 3031610924, 18568429963, 114541486785, 710973143614, 4437415155234, 27831038618735, 175318861863701, 1108762012137252, 7037137177329268, 44808588430903068
Offset: 0
The length 4 inversion sequences avoiding (120, 201, 210) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0100, 0101, 0102, 0103, 0110, 0111, 0112, 0113, 0121, 0122, 0123.
Cf.
A000108,
A057552,
A263777,
A263778,
A263779,
A263780,
A279551,
A279552,
A279553,
A279554,
A279555,
A279556,
A279557,
A279558,
A279559,
A279560,
A279561,
A279562,
A279563,
A279564,
A279565,
A279566,
A279567,
A279568,
A279569,
A279570,
A279571,
A279573.
A366114
Expansion of (1/x) * Series_Reversion( x*(1+x+x^2)/(1+x)^3 ).
Original entry on oeis.org
1, 2, 4, 7, 9, 2, -34, -130, -284, -284, 730, 4864, 14860, 27134, 6462, -170865, -771303, -2005828, -2751028, 3491747, 36288137, 130265102, 283131062, 210905402, -1317613954, -7461822262, -22297519418, -38398674146, 10151248222, 355843715494, 1495838414326
Offset: 0
-
a(n) = sum(k=0, n\2, (-1)^k*binomial(n+k, k)*binomial(2*n-k+2, n-2*k))/(n+1);
A366070
Expansion of (1/x) * Series_Reversion( x*(1+x-x^2)/(1+x)^5 ).
Original entry on oeis.org
1, 4, 23, 155, 1143, 8932, 72682, 609348, 5227035, 45659020, 404756300, 3632075109, 32928392154, 301152242600, 2775117150576, 25741623112539, 240162703635495, 2252187478291088, 21217451539791085, 200709823787548845, 1905712342347978340
Offset: 0
-
a(n) = sum(k=0, n\2, binomial(n+k, k)*binomial(4*n-k+4, n-2*k))/(n+1);
Comments