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A047911 Number of sequences with n copies each of 1, 2, 3 and longest increasing subsequence of length 3. 3
1, 47, 1306, 31451, 729811, 16928840, 397222288, 9450343019, 227749730869, 5549991941777, 136518857557006, 3384666013449308, 84477567863100244, 2120568396642137720, 53494945450407470656, 1355345188539405424235, 34469856482096766083833, 879619709716580703808739 (list; graph; refs; listen; history; text; internal format)
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 A285237 A157359

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

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Last modified March 30 10:09 EDT 2020. Contains 333125 sequences. (Running on oeis4.)