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 A045946 #42 Dec 14 2024 07:19:44
%S A045946 0,24,84,180,312,480,684,924,1200,1512,1860,2244,2664,3120,3612,4140,
%T A045946 4704,5304,5940,6612,7320,8064,8844,9660,10512,11400,12324,13284,
%U A045946 14280,15312,16380,17484,18624,19800,21012,22260,23544,24864,26220,27612,29040,30504,32004
%N A045946 Star of David matchstick numbers: a(n) = 6*n*(3*n+1).
%C A045946 Vertical spoke of triangular spiral in A051682. - _Paul Barry_, Mar 15 2003
%H A045946 Ivan Panchenko, <a href="/A045946/b045946.txt">Table of n, a(n) for n = 0..1000</a>
%H A045946 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A045946 a(n) = 24*C(n,1) + 36*C(n,2); binomial transform of (0, 24, 36, 0, 0, 0, ...). - _Paul Barry_, Mar 15 2003
%F A045946 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=0, a(1)=24, a(2)=84. - _Harvey P. Dale_, Nov 23 2012
%F A045946 G.f.: 12*x*(2+x)/(1-x)^3. - _Ivan Panchenko_, Nov 13 2013
%F A045946 a(n) = 2*A045945(n). - _Michel Marcus_, Nov 13 2013
%F A045946 a(n) = 12*A005449(n). - _R. J. Mathar_, Feb 08 2016
%F A045946 From _Amiram Eldar_, Jan 14 2021: (Start)
%F A045946 Sum_{n>=1} 1/a(n) = 1/2 - Pi/(12*sqrt(3)) - log(3)/4.
%F A045946 Sum_{n>=1} (-1)^(n+1)/a(n) = -1/2 + Pi/(6*sqrt(3)) + log(2)/3. (End)
%F A045946 From _Elmo R. Oliveira_, Dec 12 2024: (Start)
%F A045946 E.g.f.: 6*exp(x)*x*(4 + 3*x).
%F A045946 a(n) = 6*A049451(n) = 4*A081266(n) = 3*A033580(n). (End)
%t A045946 Table[6n(3n+1),{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{0,24,84},40] (* _Harvey P. Dale_, Nov 23 2012 *)
%o A045946 (PARI) a(n)=18*n^2+6*n \\ _Charles R Greathouse IV_, Feb 19 2017
%Y A045946 Cf. A005449, A033580, A049451, A045945, A051682, A081266.
%K A045946 nonn,nice,easy
%O A045946 0,2
%A A045946 _R. K. Guy_