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.
a(n) = if(n==0, 2, 2^(n-1) + sum(m=0, n, binomial(3*n,m))) \\ Jianing Song, May 30 2022
a(n) = 2^n + sum(m=0, n+1, binomial(3*n+1,m)) \\ Jianing Song, May 30 2022
a(n) = if(n==1, 2, 2^(n-2) + sum(m=0, n-1, binomial(3*n-1, m))) \\ Jianing Song, May 30 2022
{0, 0},
{1, 1},
{0, 3, 3, 0},
{1, 7, 7, 1},
{0, 4, 15, 15, 4, 0},
{1, 11, 31, 31, 11, 1},
{0, 5, 26, 63, 63, 26, 5, 0},
{1, 16, 57, 127, 127, 57, 16, 1},
{0, 6, 42, 120, 255, 255, 120, 42, 6, 0},
{1, 22, 99, 247, 511, 511, 247, 99, 22, 1},
{0, 7, 64, 219, 502, 1023, 1023, 502, 219, 64, 7, 0}
In[97]:= Table[Join[Table[(Gamma[1-m+n] Hypergeometric2F1Regularized[1,1+2 m-n,2+m,-1])/Gamma[ -2 m+n],{m,Floor[n/2],0,-1}],Table[(Gamma[1-m+n] Hypergeometric2F1Regularized[1,1+2 m-n,2+m,-1])/Gamma[ -2 m+n],{m,0,Floor[n/2]}]],{n,0,10}]; Flatten[%]
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