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A026584 Irregular triangular array T read by rows: T(i,0) = T(i,2i) = 1 for i >= 0; T(i,1) = T(i,2i-1) = floor(i/2) for i >= 1; and for i >= 2 and j = 2..2i-2, T(i,j) = T(i-1,j-2) + T(i-1,j-1) + T(i-1,j) if i+j is odd, and T(i,j) = T(i-1,j-2) + T(i-1,j) if i+j is even. 26
1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 1, 4, 2, 4, 1, 1, 1, 2, 5, 7, 8, 7, 5, 2, 1, 1, 2, 8, 9, 20, 14, 20, 9, 8, 2, 1, 1, 3, 9, 19, 28, 43, 40, 43, 28, 19, 9, 3, 1, 1, 3, 13, 22, 56, 62, 111, 86, 111, 62, 56, 22, 13, 3, 1, 1, 4, 14, 38, 69, 140, 167, 259, 222, 259 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Row sums are in A026597. - Philippe Deléham, Oct 16 2006

T(n, k) = number of integer strings s(0)..s(n) such that s(0) = 0, s(n) = n-k, |s(i)-s(i-1)| <= 1 if s(i-1) odd, |s(i)-s(i-1)| = 1 if s(i-1) is even, for i = 1..n.

LINKS

Clark Kimberling, Rows 0..100, flattened

Index entries for triangles and arrays related to Pascal's triangle

EXAMPLE

First 5 rows:

  1

  1  0  1

  1  1  2  1  1

  1  1  4  2  4  1  1

  1  2  5  7  8  7  5  2  1

MATHEMATICA

z = 12; t[n_, 0] := 1; t[n_, k_] := 1 /; k == 2 n; t[n_, 1] := Floor[n/2]; t[n_, k_] := Floor[n/2] /; k == 2 n - 1; t[n_, k_] := t[n, k] = If[EvenQ[n + k], t[n - 1, k - 2] + t[n - 1, k], t[n - 1, k - 2] + t[n - 1, k - 1] + t[n - 1, k]]; u = Table[t[n, k], {n, 0, z}, {k, 0, 2 n}];

TableForm[u]   (* A026584 array *)

v = Flatten[u] (* A026584 sequence *)

CROSSREFS

Cf. A026552, A026536, A026568, A026519, A027926.

Sequence in context: A098873 A257462 A046876 * A247342 A174547 A119326

Adjacent sequences:  A026581 A026582 A026583 * A026585 A026586 A026587

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling

EXTENSIONS

Updated by Clark Kimberling, Aug 29 2014

STATUS

approved

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Last modified June 6 10:51 EDT 2020. Contains 334843 sequences. (Running on oeis4.)