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 A073371 #36 Sep 30 2022 04:27:35
%S A073371 1,2,7,16,41,94,219,492,1101,2426,5311,11528,24881,53398,114083,
%T A073371 242724,514581,1087410,2291335,4815680,10097401,21126862,44117867,
%U A073371 91963996,191384541,397682154,825190479,1710033272,3539371201,7317351686
%N A073371 Convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n >= 0, with itself.
%C A073371 PSumSIGN transform of A045883(n-1). - _Michael Somos_, Jul 10 2003
%C A073371 Numbers of the form ((6*m+4)*2^m + (-1)^(m-1)*(3*m+4))/27. - _Artur Jasinski_, Feb 09 2007
%C A073371 With [0, 0, 0] prepended, this is an "autosequence" of the first kind, whose companion is [0, 0, 2, 3, 12, 25, 66, ...], that is A099429. - _Jean-François Alcover_, Jul 10 2022
%H A073371 G. C. Greubel, <a href="/A073371/b073371.txt">Table of n, a(n) for n = 0..1000</a>
%H A073371 Wieb Bosma, <a href="http://dx.doi.org/10.5802/jtnb.301">Signed bits and fast exponentiation</a>, J. Th. Nombres de Bordeaux, 13 no. 1 (2001), p. 27-41.
%H A073371 OEIS Wiki, <a href="https://oeis.org/wiki/Autosequence">Autosequence</a>
%F A073371 a(n) = Sum_{k=0..n} b(k) * b(n-k), where b(k) = A001045(k+1).
%F A073371 a(n) = Sum_{k=0..floor(n/2)} (n-k+1) * binomial(n-k, k) * 2^k.
%F A073371 a(n) = ((n+1)*U(n+1) + 4*(n+2)*U(n))/9 with U(n) = A001045(n+1), n>=0.
%F A073371 G.f.: 1/(1 - (1+2*x)*x)^2.
%F A073371 G.f.: 1/((1+x)*(1-2*x))^2.
%F A073371 a(n) = ((5+3*n)*2^(n+2) + (7+3*n)*(-1)^n)/27.
%F A073371 a(n) = ((6*n+4)*2^(n) + (-1)^(n-1)*(3*n+4))/27. - _Artur Jasinski_, Feb 09 2007
%F A073371 E.g.f.: (1/27)*(4*(5+6*x)*exp(2*x) + (7-3*x)*exp(-x)). - _G. C. Greubel_, Sep 28 2022
%t A073371 Table[((6n+4)*2^n + (-1)^(n-1)(3n+4))/27, {n, 100}] (* _Artur Jasinski_, Feb 09 2007 *)
%o A073371 (PARI) a(n) = if(n<-3, 0, ((5+3*n)*2^(n+2)+(7+3*n)*(-1)^n)/27)
%o A073371 (Magma) [((5+3*n)*2^(n+2) + (-1)^n*(7+3*n))/27: n in [0..40]]; // _G. C. Greubel_, Sep 28 2022
%o A073371 (SageMath)
%o A073371 def A073371(n): return ((5+3*n)*2^(n+2) + (-1)^n*(7+3*n))/27
%o A073371 [A073371(n) for n in range(40)] # _G. C. Greubel_, Sep 28 2022
%Y A073371 Second (m=1) column of triangle A073370.
%Y A073371 Cf. A001045, A062111, A099429, A127976.
%K A073371 nonn,easy
%O A073371 0,2
%A A073371 _Wolfdieter Lang_, Aug 02 2002
%E A073371 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Jun 08 2007