A386670 Number of ternary strings of length 2*n that have more 0's than the combined number of 1's and 2's.

0, 1, 9, 73, 577, 4521, 35313, 275577, 2150721, 16793929, 131230609, 1026283545, 8032614625, 62921342953, 493262044977, 3869724080313, 30379987189377, 238661880787593, 1876072096450257, 14756076838714713, 116126703647975457, 914363729294862633, 7203083947383222897

Offset: 0

Author

Enrique Navarrete, Jul 28 2025

Keywords

• nonn

Examples

			a(1)=1 since the string of length 2 is 00.
a(2)=9 since the strings of length 4 are the 4 permutations of 0001, the 4 permutations of 0002, and 0000.
a(4)=577 since the strings of length 8 are (number of permutations in parentheses): 00000001 (8), 00000002 (8), 00000011 (28), 00000012 (56), 00000022 (28), 00000111 (56), 00000112 (168), 00000122 (168), 00000222 (56), 00000000 (1).
		

Crossrefs

Cf. A054554, A059304, A128417, A128418, A243019.

Formula

a(n) = Sum_{k=1..n} 2^(n-k)*binomial(2*n,n-k).

a(n) = Sum_{k=1..n} A128417(n,k).

G.f.: (1-4*x-sqrt(1-8*x))/(sqrt(1-8*x)*(sqrt(1-8*x)+12*x-1)).

a(n) = A128418(n) - A059304(n).