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 A181995 #42 Sep 08 2022 08:45:54
%S A181995 0,0,1,6,10,20,27,42,52,72,85,110,126,156,175,210,232,272,297,342,370,
%T A181995 420,451,506,540,600,637,702,742,812,855,930,976,1056,1105,1190,1242,
%U A181995 1332,1387,1482,1540,1640,1701,1806,1870,1980,2047,2162,2232,2352,2425,2550,2626,2756,2835,2970,3052,3192,3277,3422,3510,3660,3751,3906,4000,4160,4257,4422
%N A181995 a(n) = if n mod 2 = 1 then n*(n - 1) else (n - 1)^2 + (n - 2)/2.
%C A181995 Decagonal numbers (A001107) and twice second hexagonal numbers (A002943) interleaved. - _Omar E. Pol_, Aug 03 2012
%C A181995 Similar to A074377. Members of this family are A093005, A210977, A006578, A210978, this sequence, A210981, A210982. - _Omar E. Pol_, Aug 09 2012
%C A181995 Number of kites whose vertices are the vertices a regular 2n-gon. - _Halil Ibrahim Kanpak_, Nov 08 2018
%H A181995 H. L. Abbott, D. Hanson, N. Sauer, <a href="http://dx.doi.org/10.1016/0097-3165(72)90103-3">Intersection theorems for systems of sets</a>, J. Combinatorial Theory Ser. A 12 (1972), 381--389.MR0297579 (45 #6633).
%H A181995 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A181995 G.f.: -x^2*(1 + 5*x + 2*x^2)/((1 + x)^2*(x - 1)^3). - _R. J. Mathar_, Apr 06 2012
%F A181995 a(n) = n*(4*n - 5 - (-1)^n)/4. - _Luce ETIENNE_, Oct 04 2014
%F A181995 From _Wesley Ivan Hurt_, Apr 11 2016: (Start)
%F A181995 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4.
%F A181995 a(n) = Sum_{i=floor((n-1)/2)..floor(3*(n-1)/2)} i. (End)
%F A181995 E.g.f.: x^2*cosh(x) - x*(1 - 2*x)*sinh(x)/2. - _Franck Maminirina Ramaharo_, Nov 08 2018
%p A181995 f:=n->if n mod 2 = 1 then n*(n-1) else (n-1)^2+(n-2)/2; fi;
%p A181995 [seq(f(n),n=0..130)];
%t A181995 Table[n*(4*n - 5 - (-1)^n)/4, {n, 0, 80}] (* _Wesley Ivan Hurt_, Apr 11 2016 *)
%o A181995 (PARI) a(n)=n*(4*n-5-(-1)^n)/4 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A181995 (Magma) [n*(4*n - 5 - (-1)^n)/4 : n in [0..80]]; // _Wesley Ivan Hurt_, Apr 11 2016
%Y A181995 Cf. A001107, A002943, A006578, A074377, A093005.
%Y A181995 Cf. A210977, A210978, A210981, A210982.
%K A181995 nonn,easy
%O A181995 0,4
%A A181995 _N. J. A. Sloane_, Apr 05 2012