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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. 2
1, 24, 105, 2575, 115955, 7364321, 586368681, 54862627919, 5795673908453, 673174876488400, 84386541996407430, 11262879538848476760, 1584243362361105791448, 233004893382083549345048, 35610340402841609968092950, 5627093485549459958456588775 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 23 2012
STATUS
approved

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Last modified May 20 14:08 EDT 2024. Contains 372717 sequences. (Running on oeis4.)