A071992 a(n) = 3*n^2 + 2*n - 4 * Sum_{k=1..n} A003159(k).

1, 0, 1, 4, 5, 4, 1, 0, 1, 0, 1, 4, 5, 8, 13, 16, 17, 16, 17, 20, 21, 20, 17, 16, 17, 16, 13, 8, 5, 4, 1, 0, 1, 0, 1, 4, 5, 4, 1, 0, 1, 0, 1, 4, 5, 8, 13, 16, 17, 16, 17, 20, 21, 24, 29, 32, 37, 44, 49, 52, 53, 56, 61, 64, 65, 64, 65, 68, 69, 68, 65, 64, 65, 64, 65, 68, 69, 72, 77, 80

Offset: 1

Author

Benoit Cloitre, Jun 17 2002

Keywords

• easy
• nonn

Comments

0 <= a(n) <= n for any n.

Links

• John Tyler Rascoe, Table of n, a(n) for n = 1..10241
• Robert G. Wilson v, Illustration of initial terms

Crossrefs

Cf. A000695, A003159, A062880.

Programs

Python

def A003159(n): #see A003159
    return
def A071992_list(max_n):
    A,s = [],0
    for n in range(1,max_n+1):
        s += A003159(n)
        A.append(3*n**2 + 2*n - 4*s)
    return A # John Tyler Rascoe, Feb 24 2025

Formula

For any k, a(A062880(k)) = 0.

a(A000695(k)) = A000695(k).