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 A052481 #41 Aug 15 2025 22:04:19
%S A052481 1,2,8,32,112,352,1024,2816,7424,18944,47104,114688,274432,647168,
%T A052481 1507328,3473408,7929856,17956864,40370176,90177536,200278016,
%U A052481 442499072,973078528,2130706432,4647288832,10099884032,21877489664,47244640256,101737037824,218506461184
%N A052481 a(n) = 2^n*(binomial(n,2) + 1).
%C A052481 a(n) is the generalized Euler number of an (n+2)-dimensional hypercube: (number of vertices) - (number of edges) + (number of faces) = A000079(n+2) - A001787(n+2) + A001788(n+1). - _Amiram Eldar_, Nov 08 2019
%H A052481 Vincenzo Librandi, <a href="/A052481/b052481.txt">Table of n, a(n) for n = 0..200</a>
%H A052481 Jonathan F. Mason and Richard H. Hudson, <a href="https://doi.org/10.1007/978-0-306-48517-6_18">A Generalization of Euler's Formula and its Connection to Fibonacci Numbers</a>, in: Frederic T. Howard (ed.), Applications of Fibonacci Numbers, Volume 9: Proceedings of The Tenth International Research Conference on Fibonacci Numbers and Their Applications, Springer, Dordrecht, 2004, pp. 177-185, <a href="https://archive.org/details/springer_10.1007-978-0-306-48517-6/page/n199">alternative link</a>.
%H A052481 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).
%F A052481 For the sequence 1, 1, 1, 2, 8, 32, ... we have a(n) = 2^n*(n^2-5n+8)/8. - _Paul Barry_, Jun 26 2003
%F A052481 From _R. J. Mathar_, Jan 04 2011: (Start)
%F A052481 a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3).
%F A052481 G.f.: (1-4*x+8*x^2)/(1-2*x)^3. (End)
%F A052481 E.g.f.: (1 + 2*x^2)*exp(2*x). - _G. C. Greubel_, May 16 2019
%t A052481 Table[2^n (Binomial[n, 2]+1), {n,0,30}] (* _Vincenzo Librandi_, Dec 22 2016 *)
%t A052481 LinearRecurrence[{6,-12,8},{1,2,8},30] (* _Harvey P. Dale_, May 16 2019 *)
%o A052481 (Magma) [2^n*(Binomial(n,2)+1): n in [0..30]]; // _Vincenzo Librandi_, Dec 22 2016
%o A052481 (PARI) {a(n) = 2^(n-1)*(n^2-n+2)}; \\ _G. C. Greubel_, May 16 2019
%o A052481 (Sage) [2^(n-1)*(n^2-n+2) for n in (0..30)] # _G. C. Greubel_, May 16 2019
%o A052481 (GAP) List([0..30], n-> 2^(n-1)*(n^2-n+2)); # _G. C. Greubel_, May 16 2019
%Y A052481 Cf. A000079, A001787, A001788.
%K A052481 nonn,easy
%O A052481 0,2
%A A052481 _N. J. A. Sloane_, Mar 16 2000