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%I #22 Apr 29 2022 18:13:38
%S 21,31,43,57,73,91,111,133,157,183,211,241,273,307,343,381,421,463,
%T 507,553,601,651,703,757,813,871,931,993,1057,1123,1191,1261,1333,
%U 1407,1483,1561,1641,1723,1807,1893,1981,2071,2163,2257,2353,2451,2551,2653
%N Fractional part of square root of a(n) starts with 5: first term of runs.
%C Agrees with sequence A002061 (n^2-n+1 = central polygonal numbers) starting with sixth term.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = n^2 + 7*n + 13. - _Charles R Greathouse IV_, Aug 10 2010
%t Array[#^2 + 7 # + 13 &, 48] (* _Michael De Vlieger_, Aug 05 2020 *)
%t LinearRecurrence[{3,-3,1},{21,31,43},50] (* _Harvey P. Dale_, Apr 29 2022 *)
%o (PARI) a(n)=n^2+7*n+13 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A034101.
%K nonn,base,easy
%O 1,1
%A _Patrick De Geest_, Sep 15 1998
%E Offset 1 from _Alois P. Heinz_, Aug 05 2020
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