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 A129954 #25 Oct 04 2024 14:17:39
%S A129954 1,3,6,14,32,72,160,352,768,1664,3584,7680,16384,34816,73728,155648,
%T A129954 327680,688128,1441792,3014656,6291456,13107200,27262976,56623104,
%U A129954 117440512,243269632,503316480,1040187392,2147483648,4429185024
%N A129954 Second differences of A129952.
%C A129954 First differences of A129953: a(n) = A129953(n+1) - A129953(n).
%C A129954 Essentially the same as A078836: a(n) = A078836(n+4) for n > 1.
%H A129954 Vincenzo Librandi, <a href="/A129954/b129954.txt">Table of n, a(n) for n = 0..1000</a>
%H A129954 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F A129954 a(0) = 1, a(1) = 3; for n > 1, a(n) = (n+4)*2^(n-2).
%F A129954 G.f.: (1-x)*(1-2*x^2)/(1-2*x)^2.
%F A129954 Binomial transform of [1, 2, 1, 4, 1, 6, 1, 8, ...]. - _Gary W. Adamson_, Sep 29 2007
%F A129954 E.g.f.: (x + exp(2*x)*(2 + x))/2. - _Stefano Spezia_, Oct 04 2024
%o A129954 (Magma) m:=16; S:=&cat[ [ 1, 2*i ]: i in [0..m] ]; T:=[ &+[ Binomial(j-1, k-1)*S[k]: k in [1..j] ]: j in [1..2*m] ]; U:=[ T[n+1]-T[n]: n in[1..2*m-1] ]; [ U[n+1]-U[n]: n in[1..2*m-2] ]; // _Klaus Brockhaus_, Jun 17 2007
%o A129954 (PARI) {m=29; print1(1, ",", 3, ","); for(n=2, m, print1((n+4)*2^(n-2), ","))} \\ _Klaus Brockhaus_, Jun 17 2007
%o A129954 (Python)
%o A129954 def A129954(n): return n+4<<n-2 if n>1 else 2*n+1 # _Chai Wah Wu_, Oct 03 2024
%Y A129954 Cf. A129952, A129953, A078836.
%K A129954 nonn,easy
%O A129954 0,2
%A A129954 _Paul Curtz_, Jun 10 2007
%E A129954 Edited and extended by _Klaus Brockhaus_, Jun 17 2007