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A026268 Irregular triangular array T read by rows: T(i,0)=1 for i >= 0, T[1,1] = 1, T(1,2) = 1, T(2,1) = 1, T(2,2) = 1, T(3,1) = 2, T(3,2) = 2, T(3,3) = 2; and for i >= 4, T(i,1) = i-1, T(i,i) = T(i-1,i-2) + T(i-1,i-1) and T(i,j) = T(i-1,j-2) + T(i-1,j-1 )+ T(i-1,j) for j=2..i-1. 14
1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 3, 5, 6, 4, 1, 4, 9, 14, 15, 10, 1, 5, 14, 27, 38, 39, 25, 1, 6, 20, 46, 79, 104, 102, 64, 1, 7, 27, 72, 145, 229, 285, 270, 166, 1, 8, 35, 106, 244, 446, 659, 784, 721, 436, 1, 9, 44, 149, 385, 796, 1349, 1889, 2164, 1941, 1157, 1, 10, 54, 202, 578, 1330, 2530 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

a(n) = number of strings s(0)..s(n) such that s(n) = n-k, where s(0) = 0, s(1) = 1, |s(i)-s(i-1)| <= 1 for i >= 2; |s(2)-s(1)| = 1, and |s(3)-s(2)| = 1 if s(2) = 1.

LINKS

Clark Kimberling, Rows 0..100, flattened

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

EXAMPLE

First 7 rows:

1

1 ... 1

1 ... 1 ... 1

1 ... 2 ... 2 ... 2

1 ... 3 ... 5 ... 6 ... 4

1 ... 4 ... 9 ... 14 .. 27 .. 38

1 ... 5 ... 14 .. 27 .. 38 .. 39 .. 25

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], 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, A026584, A026519, A027926.

Sequence in context: A055253 A103626 A238224 * A089258 A004065 A127496

Adjacent sequences:  A026265 A026266 A026267 * A026269 A026270 A026271

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling

EXTENSIONS

Updated by Clark Kimberling, Aug 29 2014

STATUS

approved

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Last modified January 22 15:57 EST 2019. Contains 319364 sequences. (Running on oeis4.)