A327487 - OEIS

A327487

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.

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

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..77.

FORMULA

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

EXAMPLE

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

[ 0] [ 1] 1

[ 1] [ 2, -2] 0

[ 2] [ 3, -3, 2] 2

[ 3] [ 4, -4, 3, 0] 3

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

[ 5] [ 6, -6, 5, 0, 0, 0] 5

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

[ 7] [ 8, -8, 7, 0, 0, 0, 0, 0] 7

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

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

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

PROG

(SageMath)

def divsign(s, k):

if not k.divides(s): return 0

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

def A327487row(n):

s = n + 1

r = srange(s, 1, -1)

S = [-divsign(s, s)]

for k in r:

s += divsign(s, k)

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

return S

# Prints the triangle like in the example section.

for n in (0..10):

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

CROSSREFS

Cf. A327420, A327093, A057032, A069829.

Sequence in context: A288887 A154258 A253900 * A105496 A339575 A167618

Adjacent sequences: A327484 A327485 A327486 * A327488 A327489 A327490

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Sep 14 2019

STATUS

approved