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 A168673 #18 Jan 03 2024 08:51:13
%S A168673 1,4,10,20,38,74,148,298,598,1196,2390,4778,9556,19114,38230,76460,
%T A168673 152918,305834,611668,1223338,2446678,4893356,9786710,19573418,
%U A168673 39146836,78293674,156587350,313174700,626349398,1252698794,2505397588,5010795178,10021590358
%N A168673 Binomial transform of A169609.
%C A168673 Sequence and successive differences are identical to their third differences. See principal sequence A024495. Main diagonal of the array of successive differences is A083595 (1,6,8,20,36,...).
%H A168673 G. C. Greubel, <a href="/A168673/b168673.txt">Table of n, a(n) for n = 0..1000</a>
%H A168673 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2).
%F A168673 a(n+1) - 2a(n) = A130772(n).
%F A168673 a(n) = A062092(n) - A130151(n+1).
%F A168673 a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) for n > 2; a(0) = 1, a(1) = 4, a(2) = 10.
%F A168673 G.f.: (1 + x + x^2)/(1 -3*x +3*x^2 -2*x^3). - _Philippe Deléham_, Dec 03 2009
%t A168673 LinearRecurrence[{3,-3,2},{1,4,10},25] (* _G. C. Greubel_, Jul 29 2016 *)
%t A168673 RecurrenceTable[{a[0] == 1, a[1] == 4, a[2] == 10, a[n] == 3 a[n-1] - 3 a[n-2] + 2 a[n-3]}, a, {n, 40}] (* _Vincenzo Librandi_, Jul 30 2016 *)
%o A168673 (Magma) I:=[1,4,10]; [n le 3 select I[n] else 3*Self(n-1)- 3*Self(n-2)+2*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Jul 30 2016
%o A168673 (PARI) a(n)=([0,1,0; 0,0,1; 2,-3,3]^n*[1;4;10])[1,1] \\ _Charles R Greathouse IV_, Jul 30 2016
%Y A168673 Cf. A169609, A144437, A168615, A024495, A083595, A130772, A062092, A130151.
%K A168673 nonn,easy
%O A168673 0,2
%A A168673 _Paul Curtz_, Dec 02 2009
%E A168673 Edited and extended by _Klaus Brockhaus_, Dec 03 2009