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 A077866 #45 Oct 01 2022 19:33:15
%S A077866 1,2,5,8,15,22,37,52,83,114,177,240,367,494,749,1004,1515,2026,3049,
%T A077866 4072,6119,8166,12261,16356,24547,32738,49121,65504,98271,131038,
%U A077866 196573,262108,393179,524250,786393,1048536,1572823,2097110,3145685,4194260,6291411,8388562
%N A077866 Expansion of (1-x)^(-1)/(1 - x - 2*x^2 + 2*x^3).
%C A077866 Equals triangle A122196 * [1,2,4,8,16,...]. - _Gary W. Adamson_, Nov 29 2008
%C A077866 Conjecture: let b(n) be the number of subsets S of {1,2,...,n} having more than one element such that (sum of least two elements of S) = max(S). Then b(0) = b(1) = b(2) = 0 and b(n+3) = a(n) for n >= 0. - _Clark Kimberling_ Sep 27 2022
%H A077866 Harvey P. Dale, <a href="/A077866/b077866.txt">Table of n, a(n) for n = 0..1000</a>
%H A077866 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,2).
%F A077866 a(n) = 2^(n/2)*(3 + 2*sqrt(2) + (3 - 2*sqrt(2))*(-1)^n) - n - 5. - _Paul Barry_, Apr 23 2004
%F A077866 a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + 2*a(n-4); a(0)=1, a(1)=2, a(2)=5, a(3)=8. - _Harvey P. Dale_, Feb 16 2013
%F A077866 a(2n) = 3*2^(n+1) - 2(n+1) - 3 = A050488(n+1) and a(2n+1) = 2^(n+3) - 2(n+3) = A005803(n+3). Also, a(2n+1) - a(2n) = 2^(n+1) - 1 = a(2n) - a(2n - 1). - _Gregory L. Simay_, Feb 07 2021
%F A077866 E.g.f.: 6*cosh(sqrt(2)*x) + 4*sqrt(2)*sinh(sqrt(2)*x) - exp(x)*(5 + x). - _Stefano Spezia_, Feb 08 2021
%F A077866 G.f.: 1/((1 - x)^2 * (1 - 2*x^2)). - _Michael Somos_, Aug 11 2021
%e A077866 G.f. = 1 + 2*x + 5*x^2 + 8*x^3 + 15*x^4 + 22*x^5 + 37*x^6 + ... - _Michael Somos_, Aug 11 2021
%t A077866 CoefficientList[Series[(1-x)^(-1)/(1-x-2x^2+2x^3),{x,0,50}],x] (* or *) LinearRecurrence[{2,1,-4,2},{1,2,5,8},50] (* _Harvey P. Dale_, Feb 16 2013 *)
%o A077866 (PARI) Vec((1-x)^(-1)/(1-x-2*x^2+2*x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y A077866 Bisections are A005803 and A050488.
%Y A077866 Cf. A052551 (first differences), A122196.
%K A077866 nonn,easy
%O A077866 0,2
%A A077866 _N. J. A. Sloane_, Nov 17 2002