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URL: https://oeis.org/A386670

⇱ A386670 - OEIS

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A386670
Number of ternary strings of length 2*n that have more 0's than the combined number of 1's and 2's.
1
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
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
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Jul 28 2025
STATUS
approved