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

Author

Alois P. Heinz, Jun 08 2012

Keywords

• nonn
• easy

Examples

			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}.
		

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).

Crossrefs

Row n=10 of A213276.

Programs

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);

Formula

a(n) = n*(-6044030 [phone]*n -19851310*n^2 [phone]*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.