A047911 Number of sequences with n copies each of 1, 2, 3 and longest increasing subsequence of length 3.

1, 47, 1306, 31451, 729811, 16928840, 397222288, 9450343019, 227749730869, 5549991941777, 136518857557006, 3384666013449308, 84477567863100244, 2120568396642137720, 53494945450407470656, 1355345188539405424235, 34469856482096766083833, 879619709716580703808739

Offset

1,2

Comments

Old name was: Column 3 of A047909.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..700

J. D. Horton and A. Kurn, Counting sequences with complete increasing subsequences, Congressus Numerantium, 33 (1981), 75-80. MR 681905

Formula

Reference gives explicit formula.

a(n) ~ 3^(3*n+1/2) / (2*Pi*n). - Vaclav Kotesovec, Feb 21 2016

Recurrence: 2*(n-1)*n^2*(2*n - 1)*(285*n^5 - 3103*n^4 + 13059*n^3 - 26689*n^2 + 26560*n - 10304)*a(n) = (n-1)*(47595*n^8 - 576626*n^7 + 2865154*n^6 - 7617380*n^5 + 11803635*n^4 - 10846922*n^3 + 5730080*n^2 - 1580640*n + 172800)*a(n-1) - 3*(3*n - 5)*(3*n - 4)*(19095*n^7 - 201061*n^6 + 842141*n^5 - 1814447*n^4 + 2160932*n^3 - 1410228*n^2 + 459104*n - 55296)*a(n-2) + 72*(3*n - 8)*(3*n - 7)*(3*n - 5)*(3*n - 4)*(285*n^5 - 1678*n^4 + 3497*n^3 - 3280*n^2 + 1372*n - 192)*a(n-3). - Vaclav Kotesovec, Mar 03 2016

Example

a(2) = 47: 112233, 112323, 112332, 113223, 113232, 121233, 121323, 121332, 122133, 122313, 122331, 123123, 123132, 123213, 123231, 123312, 123321, 131223, 131232, 132123, 132132, 132213, 132231, 132312, 132321, 211233, 211323, 212133, 212313, 212331, 213123, 213213, 213231, 231123, 231213, 231231, 311223, 311232, 312123, 312132, 312213, 312231, 312312, 312321, 321123, 321213, 321231. - Alois P. Heinz, Feb 05 2016

Crossrefs

Cf. A047909.

Sequence in context: A010999 A182019 A270501 * A009069 A348805 A285237

Adjacent sequences: A047908 A047909 A047910 * A047912 A047913 A047914

Keyword

nonn

Author

N. J. A. Sloane

Extensions

a(7)-a(18) from Alois P. Heinz, Jan 19 2016

New name from Alois P. Heinz, Feb 11 2016

Status

approved