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 A081200 #52 Aug 27 2025 07:35:50
%S A081200 0,1,12,109,888,6841,51012,372709,2687088,19200241,136354812,
%T A081200 964249309,6798573288,47834153641,336059778612,2358521965909,
%U A081200 16540171339488,115933787267041,812299450322412,5689910849522509,39848449432985688,279034513462540441,1953718431395986212
%N A081200 6th binomial transform of (0,1,0,1,0,1,...), A000035.
%C A081200 Binomial transform of A081199.
%C A081200 Conjecture (verified up to a(9)): Number of collinear 5-tuples of points in a 5 X 5 X 5 X ... n-dimensional cubic grid. - _Ron Hardin_, May 24 2010
%C A081200 a(n) is also the total number of words of length n, over an alphabet of seven letters, of which one of them appears an odd number of times. See the Lekraj Beedassy, Jul 22 2003, comment on A006516 (4-letter case), and the Balakrishnan reference there. For the 2-, 3-, 5-, 6- and 8-letter case analogs see A131577, A003462, A005059, A081199, A081201 respectively. - _Wolfdieter Lang_, Jul 17 2017
%H A081200 Vincenzo Librandi, <a href="/A081200/b081200.txt">Table of n, a(n) for n = 0..200</a>
%H A081200 Takao Komatsu, <a href="https://doi.org/10.22436/jnsa.012.12.05">Some recurrence relations of poly-Cauchy numbers</a>, J. Nonlinear Sci. Appl., (2019) Vol. 12, Issue 12, 829-845.
%H A081200 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-35).
%F A081200 a(n) = 12*a(n-1) - 35*a(n-2), a(0) = 0, a(1) = 1.
%F A081200 G.f.: x/((1-5*x)*(1-7*x)).
%F A081200 a(n) = 7^n/2 - 5^n/2.
%F A081200 a(n) = Sum_{k=0..n-1} 7^k * 5^(n-k-1), with a(0)=0. - _Reinhard Zumkeller_, Aug 01 2010
%F A081200 a(n) = A121213(n)/2. - _Reinhard Zumkeller_, Aug 01 2010
%F A081200 E.g.f.: exp(5*x)*(exp(2*x) - 1)/2. - _Stefano Spezia_, Jun 19 2021
%e A081200 The a(2) = 12 words of length 2 over {A, B, C, D, E, F, G} with say, A, appearing an odd number of times (that is once) are: AB, AC, AD, AE, AF, AG; BA, CA, DA, EA, FA, GA. - _Wolfdieter Lang_, Jul 17 2017
%t A081200 CoefficientList[Series[x / ((1 - 5 x) (1 - 7 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Aug 07 2013 *)
%t A081200 LinearRecurrence[{12,-35},{0,1},30] (* _Harvey P. Dale_, Feb 07 2014 *)
%o A081200 (Sage) [lucas_number1(n,12,35) for n in range(0, 21)] # _Zerinvary Lajos_, Apr 27 2009
%o A081200 (Magma) [7^n/2-5^n/2: n in [0..25]]; // _Vincenzo Librandi_, Aug 07 2013
%Y A081200 Cf. A000035, A003462, A005059, A006516, A081199, A081201 (binomial transform, and 8-letter analog), A121213, A131577.
%Y A081200 Apart from offset same as A016161.
%K A081200 nonn,easy,changed
%O A081200 0,3
%A A081200 _Paul Barry_, Mar 11 2003