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 A081593 #18 Aug 30 2025 15:23:00
%S A081593 1,17,97,241,449,721,1057,1457,1921,2449,3041,3697,4417,5201,6049,
%T A081593 6961,7937,8977,10081,11249,12481,13777,15137,16561,18049,19601,21217,
%U A081593 22897,24641,26449,28321,30257,32257,34321,36449,38641,40897,43217,45601,48049,50561,53137
%N A081593 Third row of Pascal-(1,7,1) array A081582.
%H A081593 Vincenzo Librandi, <a href="/A081593/b081593.txt">Table of n, a(n) for n = 0..1000</a>
%H A081593 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A081593 a(n) = 1 - 16*n + 32*n^2.
%F A081593 G.f.: (1+7*x)^2/(1-x)^3.
%F A081593 From _Elmo R. Oliveira_, Jun 09 2025: (Start)
%F A081593 E.g.f.: exp(x)*(1 + 16*x + 32*x^2).
%F A081593 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%t A081593 CoefficientList[Series[(1 + 7 x)^2 / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 09 2013 *)
%t A081593 LinearRecurrence[{3,-3,1},{1,17,97},50] (* _Harvey P. Dale_, Aug 30 2025 *)
%o A081593 (Magma) [1-16*n+32*n^2: n in [0..40]]; // _Vincenzo Librandi_, Aug 09 2013
%o A081593 (PARI) a(n)=32*n^2-16*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A081593 Cf. A017077, A081582, A081594.
%K A081593 easy,nonn,changed
%O A081593 0,2
%A A081593 _Paul Barry_, Mar 23 2003