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URL: https://oeis.org/A392083

⇱ A392083 - OEIS

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A392083
a(n) = 2*a(n-1) + 2^(n+1) - 1, a(0) = 0.
4
0, 3, 13, 41, 113, 289, 705, 1665, 3841, 8705, 19457, 43009, 94209, 204801, 442369, 950273, 2031617, 4325377, 9175041, 19398657, 40894465, 85983233, 180355073, 377487361, 788529153, 1644167169, 3422552065, 7113539585, 14763950081, 30601641985, 63350767617
OFFSET
0,2
COMMENTS
A recurrence relation that occurs in A391958.
FORMULA
a(n) = A391958(2^n).
From Stefano Spezia, Dec 30 2025: (Start)
a(n) = n*2^(n+1) - 2^n + 1.
G.f.: x*(3 - 2*x)/((1 - 2*x)^2*(1 - x)).
E.g.f.: exp(x)*(1 + exp(x)*(4*x - 1)). (End)
MATHEMATICA
a[n_] := n*2^(n+1) - 2^n + 1; Array[a, 31, 0] (* Amiram Eldar, Dec 30 2025 *)
PROG
(Python)
def A392083(n):
if n == 0: return 0
else: return 2*A392083(n-1) + 2**(n+1) - 1
CROSSREFS
Cf. A391958.
Sequence in context: A309139 A049167 A241527 * A234387 A173867 A121162
KEYWORD
nonn,easy
AUTHOR
A.H.M. Smeets, Dec 30 2025
STATUS
approved