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 A087447 #47 Oct 03 2024 13:21:57
%S A087447 1,1,4,10,24,56,128,288,640,1408,3072,6656,14336,30720,65536,139264,
%T A087447 294912,622592,1310720,2752512,5767168,12058624,25165824,52428800,
%U A087447 109051904,226492416,469762048,973078528,2013265920,4160749568
%N A087447 a(0) = a(1) = 1; for n > 1, a(n) = (n+2)*2^(n-2).
%C A087447 Binomial transform of A005408 (with interpolated zeros). Binomial transform is A087448. a(n+2) = 2*A045623(n+1); a(n+1) = A001792(n) + (0^n - (-2)^n)/2. The sequence 1,4,10,... given by 2^n*(n+3)/2 - 0^n/2 is the binomial transform of 1,3,3,5,5,...
%C A087447 Equals real part of binomial transform of [1, 2*i, 3, 4*i, 5, 6*i, ...]; i=sqrt(-1). - _Gary W. Adamson_, Sep 21 2008
%C A087447 An elephant sequence, see A175655. For the central square 24 A[5] vectors, with decimal values between 27 and 432, lead to this sequence (without the first leading 1). For the corner squares these vectors lead to the companion sequence A057711 (without the leading 0). - _Johannes W. Meijer_, Aug 15 2010
%H A087447 Vincenzo Librandi, <a href="/A087447/b087447.txt">Table of n, a(n) for n = 0..3000</a>
%H A087447 Paul Barry, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL8/Barry/barry84.html">A Catalan Transform and Related Transformations on Integer Sequences</a>, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
%H A087447 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F A087447 a(n) = Sum_{k=0..floor(n/2)} binomial(n, 2k)*(2k+1). - _Paul Barry_, Nov 29 2004
%F A087447 From _Colin Barker_, Mar 23 2012: (Start)
%F A087447 G.f.: (1-x)*(1-2*x+2*x^2)/(1-2*x)^2.
%F A087447 a(n) = 4*a(n-1) - 4*a(n-2) for n > 3. (End)
%F A087447 E.g.f.: (1 - x + exp(2*x)*(1 + x))/2. - _Stefano Spezia_, Jan 31 2023
%t A087447 Join[{1, 1}, Table[(n + 2) 2^(n - 2), {n, 2, 30}]] (* _Harvey P. Dale_, Feb 22 2011 *)
%o A087447 (Python)
%o A087447 def A087447(n): return n+2<<n-2 if n>1 else 1 # _Chai Wah Wu_, Oct 03 2024
%Y A087447 Essentially same as A079859.
%Y A087447 Cf. A001792, A005408, A045623, A057711, A087448, A175655.
%K A087447 nonn,easy
%O A087447 0,3
%A A087447 _Paul Barry_, Sep 05 2003
%E A087447 Definition corrected (by a factor of 2) by _R. J. Mathar_, Feb 21 2009