A213289 Number of 10-length words w over n-ary alphabet such that 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.

0, 1, 323, 5168, 37993, 201975, 916966, 3771418, 14486158, 52359693, 178880725, 575581556, 1731294863, 4845394723, 12619979568, 30703918750, 70168864396, 151545355033, 311129635863, 610492421368, 1150383157925, 2090531036111, 3677200683178, 6280769764578

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

a(n) = n*(-6044030 +17209877*n -19851310*n^2 +12422410*n^3 -4715472*n^4 +1139127*n^5 -176832*n^6 +17190*n^7 -960*n^8 +24*n^9)/24.

G.f.: x*(1+312*x +1670*x^2 -1255*x^3 +15327*x^4 +38264*x^5 +81248*x^6 +406785*x^7 +520730*x^8 +2565718*x^9)/(1-x)^11.

Example

a(0) = 0: no word of length 10 is possible for an empty alphabet.
a(1) = 1: aaaaaaaaaa for alphabet {a}.
a(2) = 323: aaaaaaaaaa, aaaaaaaaab, ..., baabababab, bbbbbbbbbb for alphabet {a,b}.

Maple

a:= n-> n*(-6044030+ (17209877+ (-19851310+ (12422410+ (-4715472+ (1139127+ (-176832+ (17190+(-960+24*n) *n)*n)*n)*n)*n)*n)*n)*n)/24:
seq(a(n), n=0..40);

Crossrefs

Row n=10 of A213276.

Sequence in context: A202610 A094394 A296973 * A094409 A253708 A210056

Adjacent sequences: A213286 A213287 A213288 * A213290 A213291 A213292

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 08 2012

Status

approved