A179339 - OEIS

%I #17 Mar 03 2023 16:23:42

%S 11,221,461,1091,1571,2621,3341,4811,5771,7661,8861,11171,12611,15341,

%T 17021,20171,22091,25661,27821,31811,34211,38621,41261,46091,48971,

%U 54221,57341,63011,66371,72461,76061,82571,86411,93341,97421

%N Positive integers of the form (30*m^2+1)/11.

%C Here m = (11*(2*n-1)+3*(-1)^n)/4 for n>0.

%C More generally, (t*((11*(2*n-1)+k*(-1)^n)/4)^2 +1)/11 = ( 22*t*n*(n-1) +t*k*(2*n-1)*(-1)^n+(t*(k^2+121)+16)/22 )/8 for any natural number t == 2, 6, 7, 8, 10 (mod 11) and k = -5, -1, -9, 3, 7, respectively.

%H B. Berselli, <a href="/A179339/b179339.txt">Table of n, a(n) for n = 1..10000</a>.

%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) = (330*n*(n-1)+45*(2*n-1)*(-1)^n+89)/4.

%F G.f.: x*(11+210*x+218*x^2+210*x^3+11*x^4)/((1+x)^2*(1-x)^3).

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

%t LinearRecurrence[{1,2,-2,-1,1},{11,221,461,1091,1571},40] (* _Harvey P. Dale_, Mar 03 2023 *)

%Y Cf. A113338, A179088, A179337, A179338, A179370.

%K nonn,easy

%O 1,1

%A _Bruno Berselli_, Jul 11 2010 - Dec 10 2010