A230556
Number of involutions avoiding the pattern 4231.
Original entry on oeis.org
1, 1, 2, 4, 9, 21, 51, 128, 327, 858, 2272, 6146, 16716, 46246, 128414, 361493, 1020506, 2913060, 8335405, 24067930, 69646035
Offset: 0
Of the 26 involutions of length 5, only 53241, 42315, 52431, 52341, and 15342 contain the pattern 4231, so a(5) = 21.
A230551
Number of involutions avoiding the pattern 2431.
Original entry on oeis.org
1, 2, 4, 10, 24, 62, 154, 396, 992, 2536, 6376, 16238, 40914, 103954, 262298, 665478, 1680726, 4260262, 10766470, 27274444
Offset: 1
Of the 26 involutions of length 26, only 35142 and 52431 contain the pattern 2431, so a(5) = 24.
A121703
Number of alternating separable permutations.
Original entry on oeis.org
1, 2, 4, 8, 20, 48, 132, 344, 996, 2720, 8132, 22888, 69940, 201040, 624132, 1822136, 5725124, 16915008, 53648772, 160012232, 511360340, 1536928624, 4942300804, 14949122328, 48322714020, 146946942688, 477105960772, 1457491035944, 4750171491956, 14568377075344
Offset: 1
a(4)=8 because of the 10 alternating permutations of length 4, 2413 and 3142 are not separable.
-
nmax = 40; aa = ConstantArray[0, nmax]; aa[[1]] = 1; aa[[2]] = 2; Do[f = Sum[aa[[k]]*x^k, {k, 1, j - 1}] + koef*x^j; sol = Solve[SeriesCoefficient[f^3 - (2*x^2 - 5*x + 4)*f^2 - (4*x^3 + x^2 - 8*x)*f - (2*x^4 + 5*x^3 + 4*x^2), {x, 0, j + 2}] == 0, koef][[1]]; aa[[j]] = koef /. sol[[1]], {j, 3, nmax}]; aa (* Vaclav Kotesovec, Jul 07 2024 *)
A230552
Number of involutions avoiding the pattern 2341.
Original entry on oeis.org
1, 2, 4, 10, 25, 66, 170, 441, 1124, 2870, 7273, 18477, 46825, 118917, 301734, 766525, 1946293, 4944614, 12557685
Offset: 1
Of the 26 involutions of length 5, only 52341 contains the pattern 2341, so a(5) = 25.
A230555
Number of involutions avoiding 3421.
Original entry on oeis.org
1, 1, 2, 4, 10, 25, 66, 173, 460, 1218, 3240, 8602, 22878, 60794, 161668, 429752, 1142758, 3038173, 8078606, 21479469, 57113888
Offset: 0
Of the 26 involutions of length 5, only 45312 contains the pattern 3421, so a(5) = 25.
A230553
Number of involutions avoiding the pattern 1342.
Original entry on oeis.org
1, 1, 2, 4, 10, 24, 62, 156, 406, 1040, 2714, 7012, 18322, 47560, 124358, 323708, 846766, 2208032, 5777330, 15082372, 39469786
Offset: 0
Of the 26 involutions of length 5, only 14523 and 15342 contain the pattern 1342, so a(5) = 24.
A230554
Number of involutions avoiding the pattern 1324.
Original entry on oeis.org
1, 1, 2, 4, 9, 21, 51, 126, 321, 820, 2160, 5654, 15272, 40758, 112280, 304471, 852164, 2341980, 6640755, 18460066, 52915999
Offset: 0
Of the 26 involutions of length 5, only 21435, 13254, 13245, 14325, and 12435 contain the pattern 1324, so a(5) = 21.
Showing 1-7 of 7 results.
Comments