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%I #13 Sep 08 2022 08:45:09
%S 1,3,12,34,75,141,238,372,549,775,1056,1398,1807,2289,2850,3496,4233,
%T 5067,6004,7050,8211,9493,10902,12444,14125,15951,17928,20062,22359,
%U 24825,27466,30288,33297,36499,39900,43506,47323,51357,55614,60100
%N Subdiagonal of array of n-gonal numbers A081422.
%C One of a family of sequences with palindromic generators.
%H Vincenzo Librandi, <a href="/A081423/b081423.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = (2*n^3 + n^2 + n + 2)/2.
%F G.f.: (1 -2*x +7*x^2 -6*x^3)/(1-x)^5.
%F E.g.f.: (2 +4*x +7*x^2 +2*x^3)*exp(x)/2. - _G. C. Greubel_, Aug 14 2019
%p a := n-> (2*n^3+n^2+n+2)/2; seq(a(n), n = 0..40); # _G. C. Greubel_, Aug 14 2019
%t CoefficientList[Series[(1 -2x +7x^2 -6x^3)/(1-x)^5, {x,0,40}], x] (* _Vincenzo Librandi_, Aug 08 2013 *)
%o (Magma) [(2*n^3+n^2+n+2)/2: n in [0..40]]; // _Vincenzo Librandi_, Aug 08 2013
%o (PARI) vector(40, n, n--; (2*n^3+n^2+n+2)/2) \\ _G. C. Greubel_, Aug 14 2019
%o (Sage) [(2*n^3+n^2+n+2)/2 for n in (0..40)] # _G. C. Greubel_, Aug 14 2019
%o (GAP) List([0..40], n-> (2*n^3+n^2+n+2)/2); # _G. C. Greubel_, Aug 14 2019
%Y Cf. A081435, A081436, A081437.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Mar 21 2003
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