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A247108 Complementary Aitken's array: triangle of numbers {a(n,k), n >= 0, 0<=k<=n} read by rows, defined by a(0,0)=1, a(n,0)=-a(n-1,n-1), a(n,k)=a(n,k-1)+a(n-1,k-1). 1
1, -1, 0, 0, -1, -1, 1, 1, 0, -1, 1, 2, 3, 3, 2, -2, -1, 1, 4, 7, 9, -9, -11, -12, -11, -7, 0, 9, -9, -18, -29, -41, -52, -59, -59, -50, 50, 41, 23, -6, -47, -99, -158, -217, -267, 267, 317, 358, 381, 375, 328, 229, 71, -146, -413, 413, 680, 997, 1355, 1736 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

a(n,0) of the triangle is equal to A000587(n), the Rao Uppuluri-Carpenter numbers or complementary Bell numbers.

LINKS

Chai Wah Wu, Rows n=0..50 of triangle, flattened

D. Wuilquin, Letters to N. J. A. Sloane, August 1984

EXAMPLE

Triangle begins:

00:      1

01:     -1      0

02:      0     -1     -1

03:      1      1      0     -1

04:      1      2      3      3      2

05:     -2     -1      1      4      7      9

06:     -9    -11    -12    -11     -7      0      9

07:     -9    -18    -29    -41    -52    -59    -59    -50

08:     50     41     23     -6    -47    -99   -158   -217   -267

09:    267    317    358    381    375    328    229     71   -146   -413

PROG

(Python)

# require Python 3.2 or higher

from itertools import accumulate

A247108_list = blist = [1]

for _ in range(10**2):

....b = -blist[-1]

....blist = list(accumulate([b]+blist))

....A247108_list += blist

(Haskell)

a247108 n k = a247108_tabl !! n !! k

a247108_row n = a247108_tabl !! n

a247108_tabl = iterate (\row -> scanl (+) (- last row) row) [1]

-- Reinhard Zumkeller, Nov 22 2014

CROSSREFS

Cf. A000587, A011971, A000110.

Sequence in context: A078041 A154840 A205102 * A236439 A011154 A048466

Adjacent sequences:  A247105 A247106 A247107 * A247109 A247110 A247111

KEYWORD

sign,tabl

AUTHOR

Chai Wah Wu, Nov 19 2014

STATUS

approved

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Last modified August 21 18:38 EDT 2019. Contains 326168 sequences. (Running on oeis4.)