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

0, 13, 29, 48, 70, 95, 123, 154, 188, 225, 265, 308, 354, 403, 455, 510, 568, 629, 693, 760, 830, 903, 979, 1058, 1140, 1225, 1313, 1404, 1498, 1595, 1695, 1798, 1904, 2013, 2125, 2240, 2358, 2479, 2603, 2730, 2860, 2993, 3129, 3268, 3410, 3555, 3703, 3854, 4008

Offset: 0

Author

Torlach Rush, Feb 12 2024

Keywords

• nonn
• easy

Comments

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)).

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000
• Sela Fried, Counting r X s rectangles in nondecreasing and Smirnov words, arXiv:2406.18923 [math.CO], 2024. See p. 9.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000326, A000566, A008594, A005449, A045943, A059845, A115067, A140090, A140091, A140672, A140673, A140674, A140675, A151542, A277976.

Programs

Mathematica

Table[n(3n+23)/2,{n,0,48}] (* James C. McMahon, Feb 20 2024 *)

Python

def a(n): return n*(3*n+23)//2

Formula

a(n) = n*(3*n + 23)/2 = A277976(n)/2.

G.f.: x*(13-10*x)/(1-x)^3.

a(n) = A151542(n) + n.

a(n) = A140675(n) + 2*n.

a(n) = A140674(n) + 3*n.

a(n) = A140673(n) + 4*n.

a(n) = A140672(n) + 5*n.

a(n) = A059845(n) + 6*n.

a(n) = A140091(n) + 7*n.

a(n) = A140090(n) + 8*n.

a(n) = A115067(n) + 9*n.

a(n) = A045943(n) + 10*n.

a(n) = A005449(n) + 11*n.

a(n) = A000326(n) + A008594(n).

Sum_{n>=1} 1/a(n) = 823467/2769844 + sqrt(3)*Pi/69 -3*log(3)/23 = 0.2328608... - R. J. Mathar, Apr 23 2024

E.g.f.: exp(x)*x*(26 + 3*x)/2. - Stefano Spezia, Apr 26 2024