cp's OEIS Frontend

A370238 a(n) = n*(3*n + 23)/2.

%I A370238 #52 Jul 06 2024 10:30:41
%S A370238 0,13,29,48,70,95,123,154,188,225,265,308,354,403,455,510,568,629,693,
%T A370238 760,830,903,979,1058,1140,1225,1313,1404,1498,1595,1695,1798,1904,
%U A370238 2013,2125,2240,2358,2479,2603,2730,2860,2993,3129,3268,3410,3555,3703,3854,4008
%N A370238 a(n) = n*(3*n + 23)/2.
%C A370238 a(a(1)) = A000566(a(1)). This is also true for each of the sequences provided in the formulae below; e.g., A151542(A151542(1)) = A000566(A151542(1)).
%H A370238 Michael De Vlieger, <a href="/A370238/b370238.txt">Table of n, a(n) for n = 0..10000</a>
%H A370238 Sela Fried, <a href="https://arxiv.org/abs/2406.18923">Counting r X s rectangles in nondecreasing and Smirnov words</a>, arXiv:2406.18923 [math.CO], 2024. See p. 9.
%H A370238 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A370238 a(n) = n*(3*n + 23)/2 = A277976(n)/2.
%F A370238 G.f.: x*(13-10*x)/(1-x)^3.
%F A370238 a(n) = A151542(n) + n.
%F A370238 a(n) = A140675(n) + 2*n.
%F A370238 a(n) = A140674(n) + 3*n.
%F A370238 a(n) = A140673(n) + 4*n.
%F A370238 a(n) = A140672(n) + 5*n.
%F A370238 a(n) = A059845(n) + 6*n.
%F A370238 a(n) = A140091(n) + 7*n.
%F A370238 a(n) = A140090(n) + 8*n.
%F A370238 a(n) = A115067(n) + 9*n.
%F A370238 a(n) = A045943(n) + 10*n.
%F A370238 a(n) = A005449(n) + 11*n.
%F A370238 a(n) = A000326(n) + A008594(n).
%F A370238 Sum_{n>=1} 1/a(n) = 823467/2769844 + sqrt(3)*Pi/69 -3*log(3)/23 = 0.2328608... - _R. J. Mathar_, Apr 23 2024
%F A370238 E.g.f.: exp(x)*x*(26 + 3*x)/2. - _Stefano Spezia_, Apr 26 2024
%t A370238 Table[n(3n+23)/2,{n,0,48}] (* _James C. McMahon_, Feb 20 2024 *)
%o A370238 (Python)
%o A370238 def a(n): return n*(3*n+23)//2
%Y A370238 Cf. A000326, A000566, A008594, A005449, A045943, A059845, A115067, A140090, A140091, A140672, A140673, A140674, A140675, A151542, A277976.
%K A370238 nonn,easy
%O A370238 0,2
%A A370238 _Torlach Rush_, Feb 12 2024