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 A321483 #36 Mar 18 2022 13:34:58
%S A321483 8,13,29,55,113,223,449,895,1793,3583,7169,14335,28673,57343,114689,
%T A321483 229375,458753,917503,1835009,3670015,7340033,14680063,29360129,
%U A321483 58720255,117440513,234881023,469762049,939524095,1879048193,3758096383,7516192769,15032385535
%N A321483 a(n) = 7*2^n + (-1)^n.
%C A321483 Difference table:
%C A321483 8, 13, 29, 55, 113, 223, 449, ...
%C A321483 5, 16, 26, 58, 110, 226, 446, 898, ...
%C A321483 11, 10, 32, 52, 116, 220, 452, 892, 1796, ...
%C A321483 -1, 22, 20, 64, 104, 232, 440, 904, 1784, 3592, ...
%C A321483 -2, 44, 40, 128, 208, 464, 880, 1808, 3568, 7184, ...
%C A321483 etc.
%C A321483 Every diagonal is a sequence of the form k*2^m.
%C A321483 a(n) is divisible by
%C A321483 . 5 if n is a term of A004767,
%C A321483 . 11 if n is a term of A016885,
%C A321483 . 13 if n is a term of A017533.
%H A321483 Colin Barker, <a href="/A321483/b321483.txt">Table of n, a(n) for n = 0..1000</a>
%H A321483 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).
%F A321483 O.g.f.: (8 + 5*x) / ((1 + x)*(1 - 2*x)). - _Colin Barker_, Nov 11 2018
%F A321483 E.g.f.: exp(-x) + 7*exp(2*x). - _Stefano Spezia_, Nov 12 2018
%F A321483 a(n) = a(n-1) + 2*a(n-2).
%F A321483 a(n) = 2*a(n-1) + 3*(-1)^n for n>0, a(0)=8.
%F A321483 a(2*k) = 7*4^k + 1, a(2*k+1) = 14*4^k - 1.
%F A321483 a(n) = A014551(n) + A014551(n-1) + A014551(n-2).
%F A321483 a(n) = 2^(n+3) - 3*A001045(n).
%F A321483 a(n) mod 9 = A070366(n+3).
%F A321483 a(n) + a(n+1) = 21*2^n.
%t A321483 a[n_] := 7*2^n + (-1)^n ; Array[a, 32, 0] (* _Amiram Eldar_, Nov 12 2018 *)
%t A321483 CoefficientList[Series[E^-x + 7 E^(2 x), {x, 0, 20}], x]*Table[n!, {n, 0, 20}] (* _Stefano Spezia_, Nov 12 2018 *)
%t A321483 LinearRecurrence[{1,2},{8,13},40] (* _Harvey P. Dale_, Mar 18 2022 *)
%o A321483 (PARI) Vec((8 + 5*x) / ((1 + x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, Nov 11 2018
%Y A321483 Cf. A000079, A001045, A005029, A010710, A014551, A062092, A062510, A070366, A175805, A199207, A206372.
%Y A321483 Cf. A033999, A005009.
%Y A321483 Subsequence of A001651, A160543, A160544.
%K A321483 nonn,easy
%O A321483 0,1
%A A321483 _Paul Curtz_, Nov 11 2018
%E A321483 Two terms corrected, and more terms added by _Colin Barker_, Nov 11 2018