%I #51 Apr 12 2026 08:44:09

%S 1,2,14,17,41,46,82,89,137,146,206,217,289,302,386,401,497,514,622,

%T 641,761,782,914,937,1081,1106,1262,1289,1457,1486,1666,1697,1889,

%U 1922,2126,2161,2377,2414,2642,2681,2921,2962,3214,3257,3521,3566,3842,3889

%N Numbers k such that 7*k + 2 is a square.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).

%F a(n) = (A047341(n)^2 - 2)/7. - _Amiram Eldar_, Aug 12 2024

%F From _Elmo R. Oliveira_, Apr 11 2026: (Start)

%F a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 5.

%F G.f.: x*(1 + x + 10*x^2 + x^3 + x^4)/((1 - x)^3*(1 + x)^2). (End)

%t ((Table[7*n + {3, 4}, {n, 0, 23}] // Flatten)^2 - 2)/7 (* _Amiram Eldar_, Aug 12 2024 *)

%o (Magma) [k: k in [0..4000] | IsSquare(7*k + 2)];

%Y The numbers k such that (m + (9-m)*k) is a square: A000217 (m = 1), this sequence (m = 2), A003154 (m = 3), A195162 (m = 4), A028387 (m = 5), A100536 (m = 6), A059993 (m = 7), A028884 (m = 8).

%Y Cf. A047341.

%K nonn,easy,changed

%O 1,2

%A _Juri-Stepan Gerasimov_, Aug 12 2024