A367545 - OEIS

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A367545

a(n) = Sum_{k=0..n} (-2)^k * |(n - k | k)|, where (a | b) denotes the Kronecker symbol.

0, -1, -2, 2, -10, 10, -34, 42, -170, 114, -650, 682, -2210, 2730, -10794, 6290, -43690, 43690, -141474, 174762, -666250, 449778, -2794154, 2796202, -9054370, 10168010, -44731050, 29826162, -176859690, 178956970, -545925250, 715827882, -2863311530, 1904682098

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..33.

FORMULA

a(n) = Sum_{k=0..n} [gcd(k, n) = 1] * (-2)^k, where [] is the Iverson bracket.

MAPLE

KS := (n, k) -> NumberTheory:-KroneckerSymbol(n, k):

A367545 := n -> local k; add((-2)^k * abs(KS(n - k , k)), k = 0..n):

seq(A367545(n), n = 0..33);

MATHEMATICA

A367545[n_]:=Sum[(-2)^k*Boole[CoprimeQ[n, k]], {k, 0, n}];

Array[A367545, 50, 0] (* Paolo Xausa, Nov 24 2023 *)

PROG

(SageMath). # For Python include 'import math' for math.gcd.

def a(n):

cop = [int(gcd(i, n) == 1) for i in range(n + 1)]

return sum(p * (-2)^k for k, p in enumerate(cop))

print([a(n) for n in range(34)])

(PARI) a(n) = sum(k=0, n, (-2)^k*abs(kronecker(n-k, k))); \\ Michel Marcus, Nov 23 2023

(Python)

from math import gcd

def A367545(n): return sum((-(1<<k) if k&1 else 1<<k) for k in range(n+1) if gcd(n, k)==1) # Chai Wah Wu, Nov 24 2023

CROSSREFS

Cf. A217831, A000010, A023896, A055034, A349136, A367544, A367546.

Sequence in context: A216708 A032005 A147801 * A263053 A361835 A066965

Adjacent sequences: A367542 A367543 A367544 * A367546 A367547 A367548

KEYWORD

sign

AUTHOR

Peter Luschny, Nov 22 2023

STATUS

approved