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 A026670 Triangular array T read by rows: T(n,0) = T(n,n) = 1 for n >= 0; for n >= 1, T(n,1) = T(n,n-1) = n+1; for n >= 2, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if n is even and k = n/2, else T(n,k) = T(n-1,k-1) + T(n-1,k). 17
 1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 5, 11, 5, 1, 1, 6, 16, 16, 6, 1, 1, 7, 22, 43, 22, 7, 1, 1, 8, 29, 65, 65, 29, 8, 1, 1, 9, 37, 94, 173, 94, 37, 9, 1, 1, 10, 46, 131, 267, 267, 131, 46, 10, 1, 1, 11, 56, 177, 398, 707, 398, 177, 56, 11, 1, 1, 12, 67 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Table of n, a(n) for n=0..68. Rob Arthan, Comments on A026674, A026725, A026670 FORMULA T(n, k) = number of paths from (0, 0) to (n-k, k) in the directed graph having vertices (i, j) and edges (i, j)-to-(i+1, j) and (i, j)-to-(i, j+1) for i, j >= 0 and edges (i, j)-to-(i+1, j+1) for i=j. EXAMPLE E.g., 11 = T(4, 2) = T(3, 1) + T(2, 2) + T(3, 2) = 4 + 3 + 4. Triangle begins: 1 1 1 1 3 1 1 4 4 1 1 5 11 5 1 1 6 16 16 6 1 1 7 22 43 22 7 1 1 8 29 65 65 29 8 1 1 9 37 94 173 94 37 9 1 1 10 46 131 267 267 131 46 10 1 1 11 56 177 398 707 398 177 56 11 1 1 12 67 233 575 1105 1105 575 233 67 12 1 ... - Philippe Deléham, Feb 02 2014 CROSSREFS Cf. A026674. Sequence in context: A050177 A013580 A147290 * A131402 A238498 A026626 Adjacent sequences: A026667 A026668 A026669 * A026671 A026672 A026673 KEYWORD nonn,tabl AUTHOR Clark Kimberling EXTENSIONS Formula corrected by David Perkinson (davidp(AT)reed.edu), Sep 19 2001 and also by Rob Arthan, Jan 16 2003 Typo in name corrected by Sean A. Irvine, Oct 09 2019 Offset corrected by R. J. Mathar and Sean A. Irvine, Oct 25 2019 STATUS approved

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Last modified September 15 10:10 EDT 2024. Contains 375932 sequences. (Running on oeis4.)