This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A351353 #17 Sep 04 2025 14:55:48
%S A351353 1,11,29,199,521,3571,9349,64079,167761,1149851,3010349,20633239,
%T A351353 54018521,370248451,969323029,6643838879,17393796001,119218851371,
%U A351353 312119004989,2139295485799,5600748293801,38388099893011,100501350283429,688846502588399,1803423556807921
%N A351353 Numbers k such that k^2 is a centered 40-gonal number.
%C A351353 All terms are Lucas numbers (A000032).
%C A351353 Corresponding indices of centered 40-gonal numbers are listed in A351354.
%H A351353 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,18,0,-1).
%F A351353 a(n) = A000032(A007310(n)).
%F A351353 G.f.: x*(1 + 11*x + 11*x^2 + x^3)/((1 + 4*x - x^2)*(1 - 4*x - x^2)). - _Stefano Spezia_, Feb 12 2022
%F A351353 E.g.f.: exp(-2*x)*(exp(2*x) + (exp(4*x) - 2)*cosh(sqrt(5)*x) - sqrt(5)*sinh(sqrt(5)*x)). - _Stefano Spezia_, Sep 03 2025
%e A351353 29 is in the sequence because 29^2 = 841 is a centered 40-gonal number (the 3rd centered 40-gonal number).
%e A351353 3571^2 = 12752041 is a centered 40-gonal number (the 799th centered 40-gonal number). Hence 3571 is in the sequence.
%p A351353 a[1] := 1: a[2] := 11: a[3] := 29: a[4] := 199: a[5] := 521:
%p A351353 for n from 6 to 25 do a[n] := a[n - 1] + 18*a[n - 2] - 18*a[n - 3] - a[n - 4] + a[n - 5]: od:
%p A351353 seq(a[n], n = 1 .. 25);
%t A351353 LinearRecurrence[{0, 18, 0, -1}, {1, 11, 29, 199}, 25] (* _Amiram Eldar_, Feb 09 2022 *)
%Y A351353 Cf. A195317, A007310, A000032.
%K A351353 nonn,easy,changed
%O A351353 1,2
%A A351353 _Lamine Ngom_, Feb 08 2022