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%I #15 Feb 19 2023 03:36:07
%S 10,108,304,598,990,1480,2068,2754,3538,4420,5400,6478,7654,8928,
%T 10300,11770,13338,15004,16768,18630,20590,22648,24804,27058,29410,
%U 31860,34408,37054,39798,42640,45580,48618,51754,54988,58320,61750,65278,68904,72628,76450
%N a(n) = (7*n+2)*(7*n+5) = 49*n^2 + 49*n + 10.
%C Cf. comment of Reinhard Zumkeller in A177059: in general, (h*n+h-k)*(h*n+k)=h^2*A002061(n+1)+(h-k)*k-h^2; therefore a(n)=49*A002061(n+1)-39. - _Bruno Berselli_, Aug 24 2010
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 98*n + a(n-1) with a(0) = 10.
%F From _Amiram Eldar_, Feb 19 2023: (Start)
%F a(n) = A017005(n)*A017041(n).
%F Sum_{n>=0} 1/a(n) = tan(3*Pi/14)*Pi/21.
%F Product_{n>=0} (1 - 1/a(n)) = sec(3*Pi/14)*cos(sqrt(13)*Pi/14).
%F Product_{n>=0} (1 + 1/a(n)) = sec(3*Pi/14)*cos(sqrt(5)*Pi/14). (End)
%e For n=1, a(1) = 98 + 10 = 108.
%e For n=2, a(2) = 98*2 + 108 = 304.
%e For n=3, a(3) = 98*3 + 304 = 598.
%t a[n_] := (7*n + 2)*(7*n + 5); Array[a, 40, 0] (* _Amiram Eldar_, Feb 19 2023 *)
%o (PARI) a(n)=49*n*(n+1)+10 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A002061, A017005, A017041, A177059.
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, May 31 2010
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