OFFSET
1,1
COMMENTS
The previous name was "a(1) = 4; then add 1 to the first number, then 2, then 3 and so on".
Numbers m such that 8m-31 is a square. - Bruce J. Nicholson, Jul 25 2017
a(n) is the minimal number of vertices for a polyhedron with at least one vertex of degree k and at least one k-gonal face for each k=3..n+2. - Riccardo Maffucci, Aug 03 2021
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
R. W. Maffucci, Self-dual polyhedra of given degree sequence, arXiv:2108.01058 [math.CO], 2021.
Ângela Mestre and José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.
Augustine O. Munagi, Integer Compositions and Higher-Order Conjugation, J. Int. Seq., Vol. 21 (2018), Article 18.8.5.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = (n^2 - n + 8)/2. - Benoit Cloitre.
From R. J. Mathar, Oct 01 2008: (Start)
G.f.: x*(4 -7*x +4*x^2)/(1-x)^3.
a(n) = a(n-1) + n - 1.
a(n) = 4 + A000217(n-1). (End)
a(n) = 4 + C(n,2), n>=1. - Zerinvary Lajos, Mar 12 2009
Sum_{n>=1} 1/a(n) = 2*Pi*tanh(sqrt(31)*Pi/2)/sqrt(31). - Amiram Eldar, Dec 13 2022
MAPLE
MATHEMATICA
Nest[Append[#, #[[-1]] + Length@ #] &, {4}, 66] (* or *)
Rest@ CoefficientList[Series[x (4 - 7 x + 4 x^2)/(1 - x)^3, {x, 0, 67}], x] (* Michael De Vlieger, Jan 23 2019 *)
PROG
(Sage)[4+binomial(n, 2) for n in range(1, 68)] # Zerinvary Lajos, Mar 12 2009
(PARI) x='x+O('x^50); Vec(x*(4 -7*x +4*x^2)/(1-x)^3) \\ G. C. Greubel, Feb 18 2017
(Magma) [(n^2 - n + 8)/2 : n in [1..50]]; // Wesley Ivan Hurt, Mar 25 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jayanth (mergujayanth(AT)yahoo.com), Sep 29 2008
EXTENSIONS
More terms from Alexander R. Povolotsky, Sep 29 2008
Edited by Benoit Cloitre and R. J. Mathar, Sep 30 2008
New name from Hugo Pfoertner, Aug 03 2021
STATUS
approved