A339771 a(n) = Sum_{i=0..n} Sum_{j=0..n} 2^max(i,j).

1, 7, 27, 83, 227, 579, 1411, 3331, 7683, 17411, 38915, 86019, 188419, 409603, 884739, 1900547, 4063235, 8650755, 18350083, 38797315, 81788931, 171966467, 360710147, 754974723, 1577058307, 3288334339, 6845104131, 14227079171, 29527900163, 61203283971

Offset: 0

Author

Bernard Schott, Dec 16 2020

Keywords

• nonn
• easy

Examples

			a(3) = 5*2^4 + 3 = 83.
		

References

• Eric Billault, Walter Damin, Robert Ferréol, Rodolphe Garin, MPSI Classes Prépas - Khôlles de Maths, Exercices corrigés, Ellipses, 2012, exercice 2.22 (2), pp. 26, 43-44.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Crossrefs

Cf. A142964 (with min instead of max).

Cf. A027981, A066524.

Partial sums of A014480.

Programs

Maple

seq((2*n-1)*2^(n+1)+3,n=0..40);

Mathematica

Table[(2*n - 1)*2^(n + 1) + 3, {n, 0, 29}] (* Amiram Eldar, Dec 16 2020 *)

PARI

a(n) = sum(i=0, n, sum(j=0, n, 2^max(i,j))); \\ Michel Marcus, Dec 16 2020

Python

def A339771():
    a, b, c = 1, 7, 27
    yield(a); yield(b)
    while True:
        yield c
        z = 4*a - 8*b + 5*c
        a, b, c = b, c, z
a = A339771()
print([next(a) for  in range(30)]) # _Peter Luschny, Dec 17 2020

Formula

a(n) = (2*n-1) * 2^(n+1) + 3.

G.f.: -(2*x+1)/((x-1)*(2*x-1)^2). - Alois P. Heinz, Dec 16 2020

E.g.f: 3*exp(x) + 2*exp(2*x)*(4*x - 1). - Stefano Spezia, Dec 16 2020

a(n) = 2*A066524(n+1) - A142964(n). - Kevin Ryde, Dec 17 2020

a(n) = (2*A027981(n)+1)/3 for n >= 1. - Hugo Pfoertner, Dec 17 2020