A327487 - OEIS

%I #23 Feb 29 2020 04:21:28

%S 1,2,-2,3,-3,2,4,-4,3,0,5,-5,4,0,2,6,-6,5,0,0,0,7,-7,6,0,0,3,0,8,-8,7,

%T 0,0,0,0,0,9,-9,8,0,0,0,4,3,0,10,-10,9,0,0,0,0,0,-3,-2,11,-11,10,0,0,

%U 0,0,5,0,-3,2,12,-12,11,0,0,0,0,0,0,0,0,0

%N T(n, k) are the summands given by the generating function of A327420(n), triangle read by rows, T(n,k) for 0 <= k <= n.

%F Sum_{k=0..n} T(n, k) = A327420(n).

%e Triangle starts (at the end of the line is the row sum (A327420)):

%e [ 0] [ 1] 1

%e [ 1] [ 2,  -2] 0

%e [ 2] [ 3,  -3,  2] 2

%e [ 3] [ 4,  -4,  3, 0] 3

%e [ 4] [ 5,  -5,  4, 0, 2] 6

%e [ 5] [ 6,  -6,  5, 0, 0, 0] 5

%e [ 6] [ 7,  -7,  6, 0, 0, 3, 0] 9

%e [ 7] [ 8,  -8,  7, 0, 0, 0, 0, 0] 7

%e [ 8] [ 9,  -9,  8, 0, 0, 0, 4, 3,  0] 15

%e [ 9] [10, -10,  9, 0, 0, 0, 0, 0, -3, -2] 4

%e [10] [11, -11, 10, 0, 0, 0, 0, 5,  0, -3, 2] 14

%o (SageMath)

%o def divsign(s, k):

%o     if not k.divides(s): return 0

%o     return (-1)^(s//k)*k

%o def A327487row(n):

%o     s = n + 1

%o     r = srange(s, 1, -1)

%o     S = [-divsign(s, s)]

%o     for k in r:

%o         s += divsign(s, k)

%o         S.append(-divsign(s, k))

%o     return S

%o # Prints the triangle like in the example section.

%o for n in (0..10):

%o     print([n], A327487row(n), sum(A327487row(n)))

%Y Cf. A327420, A327093, A057032, A069829.

%K sign,tabl

%O 0,2

%A _Peter Luschny_, Sep 14 2019