cp's OEIS Frontend

A069325 Number of 3 X n binary arrays with path of adjacent 1's from upper right corner to lower left corner.

%I A069325 #31 May 21 2023 12:38:17
%S A069325 1,8,51,295,1632,8830,47239,251261,1332456,7055228,37327007,197404203,
%T A069325 1043751584,5518106750,29171471659,154210451661,815197197636,
%U A069325 4309313949364,22779900825195,120418887728947
%N A069325 Number of 3 X n binary arrays with path of adjacent 1's from upper right corner to lower left corner.
%H A069325 Charles R Greathouse IV, <a href="/A069325/b069325.txt">Table of n, a(n) for n = 1..1383</a>
%H A069325 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (9,-21,3,24,-8,-4,4).
%F A069325 G.f.: x*(1-x+x^3)/((1-2*x-2*x^2)*(2*x^5-4*x^4+x^3+9*x^2-7*x+1)). - _Vladeta Jovovic_, Jul 02 2003
%t A069325 CoefficientList[Series[x*(1-x+x^3)/((1-2*x-2*x^2)*(2*x^5-4*x^4+x^3+9*x^2 -7*x+1)), {x, 0, 50}], x] (* _G. C. Greubel_, Apr 22 2018 *)
%t A069325 LinearRecurrence[{9,-21,3,24,-8,-4,4},{1,8,51,295,1632,8830,47239},20] (* _Harvey P. Dale_, May 21 2023 *)
%o A069325 (PARI) Vec(-x*(1-x+x^3)/(2*x^2+2*x-1)/(2*x^5-4*x^4+x^3+9*x^2-7*x+1) + O(x^99)) \\ _Charles R Greathouse IV_, Jun 12 2015
%o A069325 (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1-x+x^3)/((1-2*x-2*x^2)*(2*x^5-4*x^4+x^3+9*x^2-7*x+1)))); // _G. C. Greubel_, Apr 22 2018
%Y A069325 Row 3 of A359575.
%Y A069325 Cf. 2 X n A048739, 4 X n A069326, 5 X n A069327, 6 X n A069328, 7 X n A069329, 8 X n A069330, 9 X n A069331, 10 X n A069332, 11 X n A069333, 12 X n A069334, 13 X n A069335, 14 X n A069336, 15 X n A069337, 16 X n A069338, 17 X n A069339, 18 X n A069340, 19 X n A069341, 20 X n A069342, n X n A069343, n X n symmetric A069344.
%K A069325 nonn,easy
%O A069325 1,2
%A A069325 _R. H. Hardin_, Mar 16 2002