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%I #47 Apr 17 2024 10:55:53
%S 6,210,990,2730,5814,10626,17550,26970,39270,54834,74046,97290,124950,
%T 157410,195054,238266,287430,342930,405150,474474,551286,635970,
%U 728910,830490,941094,1061106,1190910,1330890,1481430,1642914,1815726,2000250,2196870,2405970
%N a(n) = (4n+1)(4n+2)(4n+3).
%H T. D. Noe, <a href="/A001505/b001505.txt">Table of n, a(n) for n = 0..1000</a>
%H L. B. W. Jolley, <a href="https://archive.org/details/summationofserie00joll">Summation of Series</a>, Dover, 1961
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 6 * A015219(n).
%F Sum_{n>=0} 1/a(n) = log(2)/4 = 0.17328679513998... [Jolley eq. 253. Typo fixed by _Jaume Oliver Lafont_, Jan 09 2009]
%F G.f.: 6*(1+x)*(x^2+30*x+1) / (x-1)^4. - _R. J. Mathar_, Apr 02 2011
%F Sum_{n>=0} (-1)^n/a(n) = (sqrt(2)-1)*Pi/8. - _Amiram Eldar_, Sep 17 2022
%t Table[(4n+1)(4n+2)(4n+3),{n,0,49}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 22 2012 *)
%o (Magma) [(4*n+1)*(4*n+2)*(4*n+3): n in [0..100]]; // _Vincenzo Librandi_, Apr 04 2011
%o (PARI) a(n)=(4*n+1)*(4*n+2)*(4*n+3) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A015219.
%K nonn,easy,changed
%O 0,1
%A _N. J. A. Sloane_
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