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%I A081438 #24 Sep 08 2022 08:45:09
%S A081438 1,11,36,82,155,261,406,596,837,1135,1496,1926,2431,3017,3690,4456,
%T A081438 5321,6291,7372,8570,9891,11341,12926,14652,16525,18551,20736,23086,
%U A081438 25607,28305,31186,34256,37521,40987,44660,48546,52651,56981,61542,66340
%N A081438 Diagonal in array of n-gonal numbers A081422.
%C A081438 One of a family of sequences with palindromic generators.
%H A081438 Vincenzo Librandi, Table of n, a(n) for n = 0..1000
%H A081438 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
%F A081438 a(n) = (2*n^3+9*n^2+9*n+2)/2.
%F A081438 G.f.: (1+6*x-9*x^2+2*x^3)/(1-x)^5.
%F A081438 From _Bruno Berselli_, Jun 04 2010: (Start)
%F A081438 G.f.: (1+7*x-2*x^2)/(1-x)^4 (simplified).
%F A081438 a(n) = (n+1)*(2*n^2+7*n+2)/2.
%F A081438 a(n) -4*a(n-1) +6*a(n-2) -4*a(n-3) +a(n-4) = 0, with n>3.
%F A081438 a(n) = (A177058(n+3) + A177058(n+2))/2. (End)
%F A081438 E.g.f.: (1/2)*exp(x)*(2 +20*x + 15*x^2 + 2*x^3). - _Stefano Spezia_, Aug 15 2019
%p A081438 seq((2*n^3+9*n^2+9*n+2)/2, n=0..45); # _G. C. Greubel_, Aug 14 2019
%t A081438 CoefficientList[Series[(1 +6x -9x^2 +2x^3)/(1-x)^5, {x, 0, 45}], x] (* _Vincenzo Librandi_, Aug 08 2013 *)
%t A081438 LinearRecurrence[{4,-6,4,-1},{1,11,36,82},50] (* _Harvey P. Dale_, Jan 20 2022 *)
%o A081438 (Magma) [(2*n^3+9*n^2+9*n+2)/2: n in [0..45]]; // _Vincenzo Librandi_, Aug 08 2013
%o A081438 (PARI) vector(45, n, n--; (2*n^3+9*n^2+9*n+2)/2) \\ _G. C. Greubel_, Aug 14 2019
%o A081438 (Sage) [(2*n^3+9*n^2+9*n+2)/2 for n in (0..45)] # _G. C. Greubel_, Aug 14 2019
%o A081438 (GAP) List([0..45], n-> (2*n^3+9*n^2+9*n+2)/2); # _G. C. Greubel_, Aug 14 2019
%Y A081438 Cf. A081436, A081437, A081441, A177058.
%K A081438 nonn,easy
%O A081438 0,2
%A A081438 _Paul Barry_, Mar 21 2003
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