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 A081201 #45 Aug 27 2025 07:36:00
%S A081201 0,1,14,148,1400,12496,107744,908608,7548800,62070016,506637824,
%T A081201 4113568768,33271347200,268347559936,2159841173504,17357093552128,
%U A081201 139326933401600,1117436577120256,8956419276406784,71752914167922688,574632673083392000,4600717543107198976
%N A081201 7th binomial transform of (0,1,0,1,0,1,....), A000035.
%C A081201 Binomial transform of A081200.
%C A081201 Conjecture (verified up to a(8)): Number of collinear 6-tuples of points in a 6 X 6 X 6 X... n-dimensional cubic grid. [_R. H. Hardin_, May 23 2010]
%C A081201 From _Wolfdieter Lang_, Jul 17 2017: (Start)
%C A081201 For a combinatorial interpretation of a(n) with special 8-letter words of length n see the comment in A081200 on the 7-letter analog.
%C A081201 The binomial transform of {a(n)}_{n >= 0} is A081202, the 9-letter analog.
%C A081201 (End)
%H A081201 Vincenzo Librandi, <a href="/A081201/b081201.txt">Table of n, a(n) for n = 0..200</a>
%H A081201 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-48).
%F A081201 a(n) = 14*a(n-1) - 48*a(n-2) with n>1, a(0)=0, a(1)=1.
%F A081201 G.f.: x/((1-6*x)*(1-8*x)).
%F A081201 a(n) = (1/2)*(8^n - 6^n).
%F A081201 E.g.f.: exp(7*x)*sinh(x). - _G. C. Greubel_, Nov 10 2024
%t A081201 CoefficientList[Series[x/((1 - 6 x) (1 - 8 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 07 2013 *)
%t A081201 LinearRecurrence[{14,-48},{0,1},30] (* _Harvey P. Dale_, Oct 24 2022 *)
%o A081201 (Magma) [(8^n-6^n)/2: n in [0..30]]; // _Vincenzo Librandi_, Aug 07 2013
%o A081201 (SageMath)
%o A081201 A081201=BinaryRecurrenceSequence(14,-48,0,1)
%o A081201 [A081201(n) for n in range(41)] # _G. C. Greubel_, Nov 10 2024
%Y A081201 Cf. A000035, A016169, A081200, A081202.
%Y A081201 Apart from offset same as A016170.
%K A081201 nonn,easy,changed
%O A081201 0,3
%A A081201 _Paul Barry_, Mar 11 2003
%E A081201 Name clarified by _Pontus von Brömssen_, Nov 11 2020