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 A131909 Triangle, read by rows, where T(n,k) = T(n-1,k-2) + T(n-1,k-1) for n>=k>1, with T(0,0)=1 and T(n,0) = T(n+1,1) = T(n-1,n-1) for n>0. 1
 1, 1, 1, 1, 1, 2, 2, 1, 2, 3, 3, 2, 3, 3, 5, 5, 3, 5, 5, 6, 8, 8, 5, 8, 8, 10, 11, 14, 14, 8, 13, 13, 16, 18, 21, 25, 25, 14, 22, 21, 26, 29, 34, 39, 46, 46, 25, 39, 36, 43, 47, 55, 63, 73, 85, 85, 46, 71, 64, 75, 79, 90, 102, 118, 136, 158, 158, 85, 131, 117, 135, 139, 154, 169 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS A119262(n) is the number of B-trees of order infinity with n leaves. LINKS FORMULA Row sums equal powers of 2. T(n,0) = A119262(n+1) for n>=0, where g.f. G(x) of A119262 satisfies: G(x) = x + G(x^2/(1-x)). EXAMPLE Triangle begins: 1; 1, 1; 1, 1, 2; 2, 1, 2, 3; 3, 2, 3, 3, 5; 5, 3, 5, 5, 6, 8; 8, 5, 8, 8, 10, 11, 14; 14, 8, 13, 13, 16, 18, 21, 25; 25, 14, 22, 21, 26, 29, 34, 39, 46; 46, 25, 39, 36, 43, 47, 55, 63, 73, 85; 85, 46, 71, 64, 75, 79, 90, 102, 118, 136, 158; 158, 85, 131, 117, 135, 139, 154, 169, 192, 220, 254, 294; ... Illustrate T(n,k) = T(n-1,k-2) + T(n-1,k-1): T(5,3) = T(4,1) + T(4,2) = 2 + 3 = 5; T(6,4) = T(5,2) + T(5,3) = 5 + 5 = 10; T(8,3) = T(7,1) + T(7,2) = 8 +13 = 21. PROG (PARI) T(n, k)=if(k<0 || n

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Last modified May 17 03:43 EDT 2022. Contains 353727 sequences. (Running on oeis4.)