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 A132750 #46 Feb 16 2025 08:33:06
%S A132750 1,4,9,21,49,113,257,577,1281,2817,6145,13313,28673,61441,131073,
%T A132750 278529,589825,1245185,2621441,5505025,11534337,24117249,50331649,
%U A132750 104857601,218103809,452984833,939524097,1946157057,4026531841
%N A132750 A132749 * [1, 2, 3, ...] = A007318 * A065190.
%C A132750 Equals double binomial transform of [1, 2, -3, 7, -15, 31, -63, 127, -255, ...]. - _Gary W. Adamson_, Jul 23 2008
%C A132750 For n >= 1, also the number of cliques in the n-hypercube graph Q_n. - _Eric W. Weisstein_, Mar 31 2017
%H A132750 Vincenzo Librandi, <a href="/A132750/b132750.txt">Table of n, a(n) for n = 0..1000</a>
%H A132750 V. Jelinek, T. Mansour, M. Shattuck, <a href="http://dx.doi.org/10.1016/j.aam.2012.09.002">On multiple pattern avoiding set partitions</a>, Adv. Appl. Math. 50 (2) (2013) 292-326, Lemma 4.21 (sequence starting 1, 1, 2, 4, 9, 21, .... with offset 0).
%H A132750 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Clique.html">Clique</a>
%H A132750 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>
%H A132750 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4).
%F A132750 A132749 as an infinite lower triangular matrix * vector [1, 2, 3, ...]. Binomial transform of A065190 (with an incorrect offset)
%F A132750 Row sums of triangle A135224. - _Gary W. Adamson_, Nov 23 2007
%F A132750 G.f.: (1-x-3*x^2+4*x^3)/((1-x)*(1-2*x)^2). - _Colin Barker_, Aug 09 2012
%F A132750 a(n) = n*2^(n-1) + 2^n + 1 - 0^n. - _Tim Smith_, Sep 25 2014
%F A132750 a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). - _Wesley Ivan Hurt_, Sep 26 2014
%F A132750 E.g.f.: -1 + exp(x) + (1+x)*exp(2*x). - _G. C. Greubel_, Nov 20 2019
%e A132750 a(3) = 21 = (1, 3, 3, 1) dot (1, 3, 2, 5) = (1 + 9 + 6 + 5) = 21; where A065190 = (1, 3, 2, 5, 4, 7, 6, 9, ...).
%p A132750 A132750:=n->n*2^(n-1)+2^n+1-0^n: seq(A132750(n), n=0..30); # _Wesley Ivan Hurt_, Sep 26 2014
%t A132750 Join[{1}, Table[n*2^(n-1) +2^n +1, {n, 30}]] (* _Wesley Ivan Hurt_, Sep 26 2014 *)
%t A132750 Join[{1}, LinearRecurrence[{5,-8,4}, {4,9,21}, 30]] (* _Vincenzo Librandi_, Apr 01 2017 *)
%o A132750 (Magma) [n*2^(n-1) + 2^n + 1 - 0^n : n in [0..30]]; // _Wesley Ivan Hurt_, Sep 26 2014
%o A132750 (PARI) vector(31, n, if(n==1, 1, (n-1)*2^(n-2) + 2^(n-1) + 1)) \\ _G. C. Greubel_, Nov 20 2019
%o A132750 (Sage) [1]+[n*2^(n-1) + 2^n + 1 for n in (1..30)] # _G. C. Greubel_, Nov 20 2019
%o A132750 (GAP) Concatenation([1], List([1..30], n-> n*2^(n-1) + 2^n + 1 )); # _G. C. Greubel_, Nov 20 2019
%Y A132750 Cf. A065190, A132749, A135224.
%K A132750 nonn,easy
%O A132750 0,2
%A A132750 _Gary W. Adamson_, Aug 28 2007