A392003 - OEIS

%I #30 Jan 02 2026 08:29:06

%S 0,4,7,18,35,74,147,298,595,1194,2387,4778,9555,19114,38227,76458,

%T 152915,305834,611667,1223338,2446675,4893354,9786707,19573418,

%U 39146835,78293674,156587347,313174698,626349395,1252698794,2505397587,5010795178,10021590355,20043180714

%N a(n) = (7*2^n - 9 + 5*(-1)^n) / 6.

%H Karl-Heinz Hofmann, <a href="/A392003/b392003.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).

%F Conjecture: a(2*n) = A266753(n).

%F From _Stefano Spezia_, Dec 27 2025: (Start)

%F G.f.: x^2*(4 - x)/((1 - x)*(1 + x)*(1 - 2*x)).

%F E.g.f.: exp(-x)*(exp(x) - 1)^2*(7*exp(x) + 5)/6. (End)

%t a[n_] := (7*2^n - 9 + 5*(-1)^n)/6; Array[a, 35] (* _Amiram Eldar_, Dec 27 2025 *)

%t LinearRecurrence[{2, 1, -2}, {0, 4, 7}, 34] (* _Hugo Pfoertner_, Jan 01 2026 *)

%o (Python)

%o def A392003(n): return (7*2**n - 9 + 5*(-1)**n) // 6

%Y Cf. A266753, A390768.

%K nonn,easy

%O 1,2

%A _Karl-Heinz Hofmann_, Dec 26 2025