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 A130521 Triangle, read by rows, where T(n,k) = T(n,k-1) + T(n-1,k-2) for n>=k>=2, with T(n+1,1) = T(n+1,0) = T(n,n) and T(0,0) = 1 for n>=0. 1
 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 6, 8, 11, 11, 11, 15, 19, 25, 33, 33, 33, 44, 55, 70, 89, 114, 114, 114, 147, 180, 224, 279, 349, 438, 438, 438, 552, 666, 813, 993, 1217, 1496, 1845, 1845, 1845, 2283, 2721, 3273, 3939, 4752, 5745, 6962, 8458, 8458, 8458, 10303 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS G.f. of column 0 (A127782) satisfies: G(x) = 1 + x*G(x+x^2). LINKS FORMULA T(n,0) = Sum_{k=0..[n/2]} C(n-k,k)*T(n-k-1,0) for n>0 with T(0,0)=1. For column 1, T(n,1) = Sum_{k=0..[n/2]+1} [C(n-k,k) + C(n-k+1,k-1)]*T(n-k-1,1) for n>=2, with T(0,1)=T(1,1)=1. EXAMPLE T(5,3) = T(5,2) + T(4,1) = 15 + 4 = 19; T(6,4) = T(6,3) + T(5,2) = 55 + 15 = 70; T(7,0) = T(6,6) = 89 + 25 = 114. Triangle begins: 1; 1, 1; 1, 1, 2; 2, 2, 3, 4; 4, 4, 6, 8, 11; 11, 11, 15, 19, 25, 33; 33, 33, 44, 55, 70, 89, 114; 114, 114, 147, 180, 224, 279, 349, 438; 438, 438, 552, 666, 813, 993, 1217, 1496, 1845; 1845, 1845, 2283, 2721, 3273, 3939, 4752, 5745, 6962, 8458; ... PROG (PARI) T(n, k)=if(n

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Last modified April 24 16:26 EDT 2019. Contains 322430 sequences. (Running on oeis4.)