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 A093968 #54 Feb 24 2025 11:57:18
%S A093968 0,1,2,6,8,20,24,56,64,144,160,352,384,832,896,1920,2048,4352,4608,
%T A093968 9728,10240,21504,22528,47104,49152,102400,106496,221184,229376,
%U A093968 475136,491520,1015808,1048576,2162688,2228224,4587520,4718592,9699328,9961472,20447232,20971520
%N A093968 Inverse binomial transform of n*Pell(n).
%C A093968 Binomial transform is A093967.
%C A093968 Binomial transform of (-1)^(n+1)(n*Pell(n-2)) (see A093969).
%C A093968 S-D transform of A001477 (cf. A051159). - _Philippe Deléham_, Aug 01 2006
%C A093968 a(n) is also the number of projective permutations of vertices of regular n-gons. A permutation of n vertices (AFB...CD) is considered 'projective' if there exists a line so that all the vertices can be projected onto it and the resulted points can be read in the same order: A'F'B'...C'D'. - _Anton Zakharov_, Jul 25 2016
%H A093968 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-4).
%F A093968 G.f.: x(1+2x+2x^2)/(1-2x^2)^2;
%F A093968 a(n) = 2^((n-4)/2)n((1+sqrt(2)) + (1-sqrt(2))(-1)^n).
%F A093968 a(2n) = A036289(n). a(2n+1) = A014480(n). - _R. J. Mathar_, Jun 02 2011
%F A093968 G.f.: x*G(0)/(1-x) where G(k) = 1 + x/(k+1 - 2*x*(k+1)*(k+2)/(2*x*(k+2) + 1/G(k+1) )); (recursively defined continued fraction). - _Sergei N. Gladkovskii_, Feb 01 2013
%F A093968 a(n) = n*2^floor((n-1)/2). - _Anton Zakharov_, Jul 25 2016
%F A093968 E.g.f.: x*(sqrt(2)*sinh(sqrt(2)*x) + 2*cosh(sqrt(2)*x))/2. - _Ilya Gutkovskiy_, Jul 25 2016
%F A093968 Sum_{n>=1} 1/a(n) = log(2) + sqrt(2)*log(1+sqrt(2)). - _Amiram Eldar_, Feb 13 2023
%e A093968 a(3) = 6, as there are only 6 projective permutations of vertices in a triangle ABC: ABC,CBA,ACB,BCA,CAB,BAC and it is equal to the number of simple permutations of three elements.
%e A093968 a(4) = 8, as there are only 8 permutations of vertices in a square, satisfying the projective criterion: ADBC,DACB,DCAB,CDBA,CBDA,BCAD,BACD,ABDC. ADCB is not allowed, cause there is no way to draw a line so that the projections A'B'C'D' of the original points form a line segment B'C' lying inside A'D' on this line. - _Anton Zakharov_, Jul 25 2016
%t A093968 a[n_] := n*2^Floor[(n - 1)/2]; Array[a, 40, 0] (* _Amiram Eldar_, Feb 13 2023 *)
%Y A093968 Cf. A000129, A132314.
%K A093968 easy,nonn
%O A093968 0,3
%A A093968 _Paul Barry_, Apr 21 2004