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A145018 a(n) = (n^2 - n + 8)/2. 10
4, 5, 7, 10, 14, 19, 25, 32, 40, 49, 59, 70, 82, 95, 109, 124, 140, 157, 175, 194, 214, 235, 257, 280, 304, 329, 355, 382, 410, 439, 469, 500, 532, 565, 599, 634, 670, 707, 745, 784, 824, 865, 907, 950, 994, 1039, 1085, 1132, 1180, 1229, 1279, 1330, 1382, 1435 (list; graph; refs; listen; history; text; internal format)
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
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.
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
A145018:=n->(n^2 - n + 8)/2: seq(A145018(n), n=1..100); # Wesley Ivan Hurt, Jul 25 2017
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
Cf. A000217.
Sequence in context: A234141 A093517 A248858 * A018910 A022936 A057708
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

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)