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 A081275 #30 Nov 13 2024 15:58:48
%S A081275 1,31,97,199,337,511,721,967,1249,1567,1921,2311,2737,3199,3697,4231,
%T A081275 4801,5407,6049,6727,7441,8191,8977,9799,10657,11551,12481,13447,
%U A081275 14449,15487,16561,17671,18817,19999,21217,22471,23761,25087,26449,27847,29281,30751,32257
%N A081275 Shallow diagonal of triangular spiral in A051682.
%C A081275 Reflection of A060544 in the horizontal A051682.
%C A081275 Binomial transform of (1, 30, 36, 0, 0, 0, ...).
%H A081275 Vincenzo Librandi, <a href="/A081275/b081275.txt">Table of n, a(n) for n = 0..1000</a>
%H A081275 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A081275 a(n) = C(n,0) + 30*C(n,1) + 36*C(n,2).
%F A081275 a(n) = 18*n^2 + 12*n + 1.
%F A081275 G.f.: (1 + 28*x + 7*x^2)/(1-x)^3.
%F A081275 a(0)=1, a(1)=31, a(2)=97, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Jun 30 2011
%F A081275 E.g.f.: exp(x)*(1 + 30*x + 18*x^2). - _Elmo R. Oliveira_, Nov 13 2024
%t A081275 Table[30Binomial[n,1]+36Binomial[n,2]+1,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{1,31,97},40] (* _Harvey P. Dale_, Jun 30 2011 *)
%t A081275 CoefficientList[Series[(1 + 28 x + 7 x^2) / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 07 2013 *)
%o A081275 (PARI) a(n)=18*n^2+12*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A081275 Cf. A051682, A060544, A092296.
%K A081275 nonn,easy
%O A081275 0,2
%A A081275 _Paul Barry_, Mar 15 2003