This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A386670 #19 Jul 30 2025 09:45:52
%S A386670 0,1,9,73,577,4521,35313,275577,2150721,16793929,131230609,1026283545,
%T A386670 8032614625,62921342953,493262044977,3869724080313,30379987189377,
%U A386670 238661880787593,1876072096450257,14756076838714713,116126703647975457,914363729294862633,7203083947383222897
%N A386670 Number of ternary strings of length 2*n that have more 0's than the combined number of 1's and 2's.
%F A386670 a(n) = Sum_{k=1..n} 2^(n-k)*binomial(2*n,n-k).
%F A386670 a(n) = Sum_{k=1..n} A128417(n,k).
%F A386670 G.f.: (1-4*x-sqrt(1-8*x))/(sqrt(1-8*x)*(sqrt(1-8*x)+12*x-1)).
%F A386670 a(n) = A128418(n) - A059304(n).
%e A386670 a(1)=1 since the string of length 2 is 00.
%e A386670 a(2)=9 since the strings of length 4 are the 4 permutations of 0001, the 4 permutations of 0002, and 0000.
%e A386670 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).
%Y A386670 Cf. A054554, A059304, A128417, A128418, A243019.
%K A386670 nonn
%O A386670 0,3
%A A386670 _Enrique Navarrete_, Jul 28 2025