A228344 - OEIS

A228344

a(n) = floor(3*n^2/4) - 1.

2, 5, 11, 17, 26, 35, 47, 59, 74, 89, 107, 125, 146, 167, 191, 215, 242, 269, 299, 329, 362, 395, 431, 467, 506, 545, 587, 629, 674, 719, 767, 815, 866, 917, 971, 1025, 1082, 1139, 1199, 1259, 1322, 1385, 1451, 1517, 1586, 1655, 1727, 1799, 1874, 1949, 2027

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,1

COMMENTS

This sequence has a relatively high density of primes given its simple formula and high values: 38 in the first 100. The composites in the first 157 elements are mainly p1*p2 or p1*p2^2 or p^1^3, with the rest having three distinct primes. The first composite of four distinct primes is at n = 158, a(n)= 18722 = 2*11*23*37.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

FORMULA

Floor(3n^2/4) - 1 = A007590(n) + A002620(n) - 1 = 3*A002620 - 1.

a(n) = (-11+3*(-1)^n+6*n^2)/8. a(n) = 2*a(n-1)-2*a(n-3)+a(n-4). G.f.: x^2*(x-2)*(x^2+x+1) / ((x-1)^3*(x+1)). - Colin Barker, Aug 27 2013

EXAMPLE

a(14) = floor(3*14^2/4)-1 = 146.

MATHEMATICA

Table[Floor[3*n^2/4] - 1, {n, 2, 100}] (* T. D. Noe, Aug 23 2013 *)

LinearRecurrence[{2, 0, -2, 1}, {2, 5, 11, 17}, 60] (* Harvey P. Dale, May 08 2022 *)

CROSSREFS