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

0,3

Links

Table of n, a(n) for n=0..22.

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).

Example

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.

Sequence in context: A126641 A346229 A081627 * A164588 A023001 A277672

Adjacent sequences: A386667 A386668 A386669 * A386671 A386672 A386673

Keyword

nonn

Author

Enrique Navarrete, Jul 28 2025

Status

approved