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 A328881 #35 Dec 05 2019 08:22:09 %S A328881 1,0,1,0,2,3,8,14,29,56,114,227,456,910,1821,3640,7282,14563,29128, %T A328881 58254,116509,233016,466034,932067,1864136,3728270,7456541,14913080, %U A328881 29826162,59652323,119304648,238609294,477218589,954437176,1908874354,3817748707 %N A328881 a(n+3) = 2^n - a(n), a(0)=a(2)=1, a(1)=0 for n >= 0. %C A328881 The array of a(n) and its repeated differences: %C A328881 1, 0, 1, 0, 2, 3, 8, 14, ... %C A328881 -1, 1, -1, 2, 1, 5, 6, 15, ... %C A328881 2, -2, 3, -1, 4, 1, 9, 12, ... %C A328881 -4, 5, -4, 5, -3, 8, 3, 19, ... %C A328881 9, -9, 9, -8, 11, -5, 16, 5, ... %C A328881 -18, 18, -17, 19, -16, 21, -11, 32, ... %C A328881 36, -35, 36, -35, 37, -32, 43, -21, ... %C A328881 -71, 71, -71, 72, -69, 75, -64, 85, ... %C A328881 ... %C A328881 The recurrence is the same for every row. %C A328881 From _Jean-François Alcover_, Nov 28 2019: (Start) %C A328881 It appears that, when odd, a(n) is never a multiple of 5. %C A328881 Main and 3rd upper diagonals of the difference array are A001045 (Jacobsthal numbers); first upper diagonal is negated A001045; second upper diagonal is A000079 (powers of 2); 4th upper diagonal is A062092. %C A328881 (End) %H A328881 Colin Barker, <a href="/A328881/b328881.txt">Table of n, a(n) for n = 0..1000</a> %H A328881 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,2). %F A328881 a(n+1) - 2*a(n) = period 6: repeat [-2, 1, -2, 2, -1, 2]. %F A328881 a(n+12) - a(n) = 455*2^n. %F A328881 From _Colin Barker_, Oct 29 2019: (Start) %F A328881 G.f.: (1 - 2*x + x^2 - x^3) / ((1 + x)*(1 - 2*x)*(1 - x + x^2)). %F A328881 a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4) for n>3. %F A328881 (End) %F A328881 a(n+2) - a(n) = A024495(n). %F A328881 a(n+6) - a(n) = 7*2^n. %F A328881 a(n+9) + a(n) = 57*2^n. %F A328881 a(n) = A113405(n) + A092220(n+5). %F A328881 9*a(n) = 2^n + 5*(-1)^n + 3*A010892(n). - _R. J. Mathar_, Nov 28 2019 %t A328881 a[0] = a[2] = 1; a[1] = 0; a[n_] := a[n] = 2^(n - 3) - a[n - 3]; Array[a, 36, 0] (* _Amiram Eldar_, Nov 06 2019 *) %o A328881 (PARI) Vec((1 - 2*x + x^2 - x^3) / ((1 + x)*(1 - 2*x)*(1 - x + x^2)) + O(x^40)) \\ _Colin Barker_, Oct 29 2019 %Y A328881 Cf. A024495, A062092, A131714. %Y A328881 Cf. A015565, A092220, A113405. %K A328881 nonn,easy %O A328881 0,5 %A A328881 _Paul Curtz_, Oct 29 2019