A286264 a(n) = 2*(ceiling((n^2)/2)+1) - 1.
3, 5, 11, 17, 27, 37, 51, 65, 83, 101, 123, 145, 171, 197, 227, 257, 291, 325, 363, 401, 443, 485, 531, 577, 627, 677, 731, 785, 843, 901, 963, 1025, 1091, 1157, 1227, 1297, 1371, 1445, 1523, 1601, 1683, 1765, 1851, 1937, 2027, 2117, 2211, 2305, 2403, 2501
Offset: 1
Examples
n=2: (1*3*5*7)/(2*4*6*8) = (1*1*5*7)/(2*4*2*8) => a(2) = 5 = A151800(2^2). n=3: (1*3*5*7*9*11*13*15*17)/(2*4*6*8*10*12*14*16*18) = (1*1*1*1*1*11*13*15*17)/(2*4*2*8*2*12*2*16*2) => a(3) = 11 = A151800(3^2).
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
Programs
-
Magma
[3/2 - (-1)^n/2 + n^2 : n in [1..100]]; // Wesley Ivan Hurt, May 05 2017
-
Maple
A286264:=n->3/2 - (-1)^n/2 + n^2: seq(A286264(n), n=1..100); # Wesley Ivan Hurt, May 05 2017
-
Mathematica
Table[2 (Ceiling[n^2/2] + 1) - 1, {n, 1, 40}] -
PARI
Vec(x*(3 - x + x^2 + x^3) / ((1 - x)^3*(1 + x)) + O(x^60)) \\ Colin Barker, May 05 2017
Formula
a(n) > n^2.
From Colin Barker, May 05 2017: (Start)
G.f.: x*(3 - x + x^2 + x^3) / ((1 - x)^3*(1 + x)).
a(n) = 3/2 - (-1)^n/2 + n^2.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4. (End)
Sum_{n>=1} 1/a(n) = Pi*coth(Pi/2)/4 + Pi*tanh(Pi/sqrt(2))/(4*sqrt(2)) - 1/2. - Amiram Eldar, Jul 26 2024
Extensions
More terms from Colin Barker, May 05 2017