A213874 Number of words w where each letter of the 4-ary alphabet occurs n times and for every prefix z of w we have #(z,a_i) = 0 or #(z,a_i) >= #(z,a_j) for all j>i and #(z,a_i) counts the occurrences of the i-th letter in z.

1, 24, 105, 2575, 115955, 7364321, 586368681, 54862627919, 5795673908453, 673174876488400, 84386541996407430, 11262879538848476760, 1584243362361105791448, 233004893382083549345048, 35610340402841609968092950, 5627093485549459958456588775

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..140

Formula

For n > 1, a(n) = 8*(9297776*n^10 + 17051200*n^9 - 11545329*n^8 - 20688255*n^7 + 7760028*n^6 + 7548270*n^5 - 2879537*n^4 - 619195*n^3 + 326046*n^2 - 30420*n + 216) * (4*n-5)! / (3 * (2*n-1) * (2*n+1) * (2*n+3) * (9*n^2-9*n+2) * (9*n^2+9*n+2) * (n-2)! * (n+1)! * (n+2)! * (n+3)!). - Vaclav Kotesovec, Sep 02 2014

Example

a(0) = 1: the empty word.
a(1) = 24: abcd, abdc, ..., dcab, dcba, (all permutations of 4 letters).
a(2) = 105: aabbccdd, aabbcdcd, aabbdccd, ..., dcaabbcd, dcababcd, dcbaabcd.

Mathematica

Flatten[{1, 24, Table[8*(9297776*n^10 + 17051200*n^9 - 11545329*n^8 - 20688255*n^7 + 7760028*n^6 + 7548270*n^5 - 2879537*n^4 - 619195*n^3 + 326046*n^2 - 30420*n + 216) * (4*n-5)! / (3 * (2*n-1) * (2*n+1) * (2*n+3) * (9*n^2-9*n+2) * (9*n^2+9*n+2) * (n-2)! * (n+1)! * (n+2)! * (n+3)!), {n, 2, 20}]}] (* Vaclav Kotesovec, Sep 02 2014 *)

Crossrefs

Column k=4 of A213275.

Sequence in context: A044275 A044656 A011199 * A100149 A013980 A100150

Adjacent sequences: A213871 A213872 A213873 * A213875 A213876 A213877

Keyword

nonn

Author

Alois P. Heinz, Jun 23 2012

Status

approved