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%I #22 Jan 27 2022 03:05:06
%S 390,750,1230,1830,2550,3390,4350,5430,6630,7950,9390,10950,12630,
%T 14430,16350,18390,20550,22830,25230,27750,30390,33150,36030,39030,
%U 42150,45390,48750,52230,55830,59550,63390,67350,71430,75630,79950,84390,88950,93630,98430
%N a(n) = 60*n^2 + 180*n + 150.
%C First differences of A068236, successive differences of (n+1)^5 - n^5 (A022521).
%H Vincenzo Librandi, <a href="/A069477/b069477.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=390, a(2)=750, a(3)=1230. - _Harvey P. Dale_, Apr 06 2012
%F Sum_{n>=1} 1/a(n) = (Pi/60)*tanh(Pi/2) - 1/25. - _Amiram Eldar_, Jan 27 2022
%t Table[30 (2 n^2 + 6 n + 5), {n, 1, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 19 2011 *)
%t LinearRecurrence[{3,-3,1},{390,750,1230},40] (* _Harvey P. Dale_, Apr 06 2012 *)
%o (Magma) [30*(2*n^2 + 6*n + 5): n in [1..40]]; // _Vincenzo Librandi_, Nov 23 2011
%o (PARI) a(n)=60*n^2+180*n+150 \\ _Charles R Greathouse IV_, Nov 23 2011
%Y Cf. A101096, A022521, A068236, A069477.
%K nonn,easy
%O 1,1
%A Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), Apr 11 2002