A351353 - OEIS

%I #13 Mar 23 2022 13:07:02

%S 1,11,29,199,521,3571,9349,64079,167761,1149851,3010349,20633239,

%T 54018521,370248451,969323029,6643838879,17393796001,119218851371,

%U 312119004989,2139295485799,5600748293801,38388099893011,100501350283429,688846502588399,1803423556807921

%N Numbers k such that k^2 is a centered 40-gonal number.

%C All terms are Lucas numbers (A000032).

%C Corresponding indices of centered 40-gonal numbers are listed in A351354.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,18,0,-1).

%F a(n) = A000032(A007310(n)).

%F 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

%e 29 is in the sequence because 29^2 = 841 is a centered 40-gonal number (the 3rd centered 40-gonal number).

%e 3571^2 = 12752041 is a centered 40-gonal number (the 799th centered 40-gonal number). Hence 3571 is in the sequence.

%p a[1] := 1: a[2] := 11: a[3] := 29: a[4] := 199: a[5] := 521:

%p 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 seq(a[n], n = 1 .. 25);

%t LinearRecurrence[{0, 18, 0, -1}, {1, 11, 29, 199}, 25] (* _Amiram Eldar_, Feb 09 2022 *)

%Y Cf. A195317, A007310, A000032.

%K nonn,easy

%O 1,2

%A _Lamine Ngom_, Feb 08 2022