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

%I A339771 #39 Dec 19 2020 04:46:24
%S A339771 1,7,27,83,227,579,1411,3331,7683,17411,38915,86019,188419,409603,
%T A339771 884739,1900547,4063235,8650755,18350083,38797315,81788931,171966467,
%U A339771 360710147,754974723,1577058307,3288334339,6845104131,14227079171,29527900163,61203283971
%N A339771 a(n) = Sum_{i=0..n} Sum_{j=0..n} 2^max(i,j).
%D A339771 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.
%H A339771 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4).
%F A339771 a(n) = (2*n-1) * 2^(n+1) + 3.
%F A339771 G.f.: -(2*x+1)/((x-1)*(2*x-1)^2). - _Alois P. Heinz_, Dec 16 2020
%F A339771 E.g.f: 3*exp(x) + 2*exp(2*x)*(4*x - 1). - _Stefano Spezia_, Dec 16 2020
%F A339771 a(n) = 2*A066524(n+1) - A142964(n). - _Kevin Ryde_, Dec 17 2020
%F A339771 a(n) = (2*A027981(n)+1)/3 for n >= 1. - _Hugo Pfoertner_, Dec 17 2020
%e A339771 a(3) = 5*2^4 + 3 = 83.
%p A339771 seq((2*n-1)*2^(n+1)+3,n=0..40);
%t A339771 Table[(2*n - 1)*2^(n + 1) + 3, {n, 0, 29}] (* _Amiram Eldar_, Dec 16 2020 *)
%o A339771 (PARI) a(n) = sum(i=0, n, sum(j=0, n, 2^max(i,j))); \\ _Michel Marcus_, Dec 16 2020
%o A339771 (Python)
%o A339771 def A339771():
%o A339771     a, b, c = 1, 7, 27
%o A339771     yield(a); yield(b)
%o A339771     while True:
%o A339771         yield c
%o A339771         z = 4*a - 8*b + 5*c
%o A339771         a, b, c = b, c, z
%o A339771 a = A339771()
%o A339771 print([next(a) for _ in range(30)]) # _Peter Luschny_, Dec 17 2020
%Y A339771 Cf. A142964 (with min instead of max).
%Y A339771 Cf. A027981, A066524.
%Y A339771 Partial sums of A014480.
%K A339771 nonn,easy
%O A339771 0,2
%A A339771 _Bernard Schott_, Dec 16 2020