cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A001505 a(n) = (4n+1)(4n+2)(4n+3).

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%I A001505 #51 Aug 24 2025 11:23:18
%S A001505 6,210,990,2730,5814,10626,17550,26970,39270,54834,74046,97290,124950,
%T A001505 157410,195054,238266,287430,342930,405150,474474,551286,635970,
%U A001505 728910,830490,941094,1061106,1190910,1330890,1481430,1642914,1815726,2000250,2196870,2405970
%N A001505 a(n) = (4n+1)(4n+2)(4n+3).
%H A001505 T. D. Noe, <a href="/A001505/b001505.txt">Table of n, a(n) for n = 0..1000</a>
%H A001505 L. B. W. Jolley, <a href="https://archive.org/details/summationofserie00joll">Summation of Series</a>, Dover, 1961
%H A001505 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A001505 a(n) = 6 * A015219(n).
%F A001505 Sum_{n>=0} 1/a(n) = log(2)/4 = 0.17328679513998... [Jolley eq. 253. Typo fixed by _Jaume Oliver Lafont_, Jan 09 2009]
%F A001505 G.f.: 6*(1+x)*(x^2+30*x+1) / (x-1)^4. - _R. J. Mathar_, Apr 02 2011
%F A001505 Sum_{n>=0} (-1)^n/a(n) = (sqrt(2)-1)*Pi/8. - _Amiram Eldar_, Sep 17 2022
%F A001505 E.g.f.: 2*exp(x)*(3 + 102*x + 144*x^2 + 32*x^3). - _Stefano Spezia_, Aug 24 2025
%t A001505 Table[(4n+1)(4n+2)(4n+3),{n,0,49}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 22 2012 *)
%o A001505 (Magma) [(4*n+1)*(4*n+2)*(4*n+3): n in [0..100]]; // _Vincenzo Librandi_, Apr 04 2011
%o A001505 (PARI) a(n)=(4*n+1)*(4*n+2)*(4*n+3) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A001505 Cf. A015219.
%K A001505 nonn,easy,changed
%O A001505 0,1
%A A001505 _N. J. A. Sloane_