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.
%I A204674 #24 Aug 08 2025 20:12:50
%S A204674 1,12,57,160,345,636,1057,1632,2385,3340,4521,5952,7657,9660,11985,
%T A204674 14656,17697,21132,24985,29280,34041,39292,45057,51360,58225,65676,
%U A204674 73737,82432,91785,101820,112561,124032,136257,149260,163065,177696,193177,209532,226785,244960,264081
%N A204674 a(n) = 4*n^3 + 5*n^2 + 2*n + 1.
%H A204674 Andrew Howroyd, <a href="/A204674/b204674.txt">Table of n, a(n) for n = 0..1000</a>
%H A204674 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A204674 a(n) = (4*n^2 + n + 1)*(n + 1).
%F A204674 G.f.: (1 + 3*x)*(1 + 5*x)/(1 - x)^4. - _Andrew Howroyd_, Jan 07 2020
%F A204674 E.g.f.: exp(x)*(1 + 11*x + 17*x^2 + 4*x^3). - _Elmo R. Oliveira_, Aug 08 2025
%t A204674 LinearRecurrence[{4,-6,4,-1},{1,12,57,160},50] (* or *) CoefficientList[ Series[(1+3x)(1+5x)/(1-x)^4,{x,0,50}],x] (* _Harvey P. Dale_, Jun 25 2021 *)
%o A204674 (Haskell)
%o A204674 a204674 n = n * (n * (4 * n + 5) + 2) + 1
%o A204674 (PARI) a(n)={ 4*n^3 + 5*n^2 + 2*n + 1 } \\ _Andrew Howroyd_, Jan 07 2020
%Y A204674 Row sums of A033293.
%Y A204674 Cf. A054567, A226449.
%K A204674 nonn,easy
%O A204674 0,2
%A A204674 _Reinhard Zumkeller_, Jan 18 2012
%E A204674 Terms a(26) and beyond from _Andrew Howroyd_, Jan 07 2020