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A026692 Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1<=k<=n-1, T(n,k)=T(n-1,k-1)+T(n-2,k-1)+T(n-1,k) if k or n-k is of form 2h for h=1,2,...,[ n/4 ], else T(n,k)=T(n-1,k-1)+T(n-1,k). 15
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 8, 4, 1, 1, 5, 15, 15, 5, 1, 1, 6, 24, 30, 24, 6, 1, 1, 7, 35, 54, 54, 35, 7, 1, 1, 8, 48, 89, 138, 89, 48, 8, 1, 1, 9, 63, 137, 281, 281, 137, 63, 9, 1, 1, 10, 80, 200, 507, 562, 507, 200, 80, 10, 1, 1, 11, 99, 280, 844 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..71.

FORMULA

T(n, k) = number of paths from (0, 0) to (n-k, k) in 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 odd and j >= i and for j odd and i >= j.

EXAMPLE

Triangle begins:

  1;

  1, 1;

  1, 2,  1;

  1, 3,  3,  1;

  1, 4,  8,  4, 1;

  1, 5, 15, 15, 5, 1;

  ...

MATHEMATICA

T[_, 0] = 1; T[n_, n_] = 1; T[n_, k_] /; EvenQ[k] && 1 <= k/2 <= Floor[n/4] || EvenQ[n-k] && 1 <= (n-k)/2 <= Floor[n/4] := T[n, k] = T[n-1, k-1] + T[n-2, k-1] + T[n-1, k]; T[n_, k_] := T[n, k] = T[n-1, k-1] + T[n-1, k];

Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Jul 02 2017 *)

CROSSREFS

Sequence in context: A169945 A073134 A300260 * A114202 A125806 A202756

Adjacent sequences:  A026689 A026690 A026691 * A026693 A026694 A026695

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified April 25 23:48 EDT 2019. Contains 322465 sequences. (Running on oeis4.)