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A225413 Triangle read by rows: T(n,k) = (A101164(n,k) - A014473(n,k))/2. 2
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 6, 12, 6, 0, 0, 0, 0, 10, 30, 30, 10, 0, 0, 0, 0, 15, 60, 91, 60, 15, 0, 0, 0, 0, 21, 105, 215, 215, 105, 21, 0, 0, 0, 0, 28, 168, 435, 590, 435, 168, 28, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,18

COMMENTS

Has opposite parity to A140356, A155454.

LINKS

Reinhard Zumkeller, Rows n = 0..100 of table, flattened

FORMULA

T(n,k) = (A101164(n,k) - A014473(n,k))/2

       = (A008288(n,k) - 2*A007318(n,k) + 1)/2

EXAMPLE

0

0, 0

0, 0, 0

0, 0, 0, 0

0, 0, 1, 0, 0

0, 0, 3, 3, 0, 0

0, 0, 6, 12, 6, 0, 0

0, 0, 10, 30, 30, 10, 0, 0

0, 0, 15, 60, 91, 60, 15, 0, 0

0, 0, 21, 105, 215, 215, 105, 21, 0, 0

0, 0, 28, 168, 435, 590, 435, 168, 28, 0, 0

0, 0, 36, 252, 791, 1365, 1365, 791, 252, 36, 0, 0

0, 0, 45, 360, 1330, 2800, 3571, 2800, 1330, 360, 45, 0, 0

0, 0, 55, 495, 2106, 5250, 8197, 8197, 5250, 2106, 495, 55, 0, 0

0, 0, 66, 660, 3180, 9180, 17038, 20888, 17038, 9180, 3180, 660, 66, 0, 0

PROG

(Haskell)

a225413 n k = a225413_tabl !! n !! k

a225413_row n = a225413_tabl !! n

a225413_tabl = map (map (`div` 2)) $

               zipWith (zipWith (-)) a101164_tabl a014473_tabl

-- Reinhard Zumkeller, Jul 30 2013

CROSSREFS

Cf. A007318, A008288, A014473, A101164, A140356, A155454.

3rd column = A000217 (triangular numbers).

4th column = A027480 (n(n+1)(n+2)/2).

Sequence in context: A318330 A199261 A110492 * A180995 A144331 A216805

Adjacent sequences:  A225410 A225411 A225412 * A225414 A225415 A225416

KEYWORD

nonn,easy,tabl

AUTHOR

Jeremy Gardiner, Jul 28 2013

STATUS

approved

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Last modified November 14 22:17 EST 2019. Contains 329134 sequences. (Running on oeis4.)