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A028262 Elements in 3-Pascal triangle (by row). 22
1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 5, 8, 5, 1, 1, 6, 13, 13, 6, 1, 1, 7, 19, 26, 19, 7, 1, 1, 8, 26, 45, 45, 26, 8, 1, 1, 9, 34, 71, 90, 71, 34, 9, 1, 1, 10, 43, 105, 161, 161, 105, 43, 10, 1, 1, 11, 53, 148, 266, 322, 266, 148, 53, 11, 1, 1, 12, 64, 201, 414, 588, 588, 414, 201, 64 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

T(n+2,k+1) = A007318(n,k) - A007318(n+2,k+1); 0 < k < n. - Reinhard Zumkeller, Aug 02 2012

LINKS

Reinhard Zumkeller, >Rows n = 0..150 of triangle, flattened

László Németh, Tetrahedron trinomial coefficient transform, Integers (2019) Vol. 19, Article A41.

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

FORMULA

After the 3rd row, use Pascal's rule.

T(n, k) = C(n, k) + C(n-2, k-1). G.f.: (1+x^2y) / [1-x(1+y)]. - Ralf Stephan, Jan 31 2005

EXAMPLE

1; 1 1; 1 3 1; 1 4 4 1; 1 5 8 5 1; ...

MATHEMATICA

T[n_, k_] := If[n == 1, 1, Binomial[n, k] + Binomial[n-2, k-1]]; Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 28 2015 *)

PROG

(Haskell)

a028262 n k = a028262_tabl !! n !! k

a028262_row n = a028262_tabl !! n

a028262_tabl = [1] : [1, 1] : iterate

   (\row -> zipWith (+) ([0] ++ row) (row ++ [0])) [1, 3, 1]

-- Reinhard Zumkeller, Aug 02 2012

CROSSREFS

Cf. A072405, A028275.

Sequence in context: A077228 A049687 A132735 * A173117 A050177 A013580

Adjacent sequences:  A028259 A028260 A028261 * A028263 A028264 A028265

KEYWORD

nonn,nice,tabl

AUTHOR

Mohammad K. Azarian

EXTENSIONS

More terms from James A. Sellers

STATUS

approved

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Last modified October 13 20:38 EDT 2019. Contains 327981 sequences. (Running on oeis4.)