A386858 a(n) = floor(5*n^2/8).

0, 2, 5, 10, 15, 22, 30, 40, 50, 62, 75, 90, 105, 122, 140, 160, 180, 202, 225, 250, 275, 302, 330, 360, 390, 422, 455, 490, 525, 562, 600, 640, 680, 722, 765, 810, 855, 902, 950, 1000, 1050, 1102, 1155, 1210, 1265, 1322, 1380, 1440, 1500, 1562, 1625, 1690, 1755

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

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

Formula

a(2n) = A032526(n).

a(2n+1) = A028895(n).

a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) for n > 6.

G.f.: -x^2*(2*x^2 + x + 2)/((x - 1)^3*(x + 1)*(x^2 + 1)).

Sum_{n>=2} 1/a(n) = 2/5 + Pi^2/60 + tan(Pi/(2*sqrt(5)))*Pi/(2*sqrt(5)). - Amiram Eldar, Aug 15 2025

Mathematica

A386858[n_] := Floor[5*n^2/8]; Array[A386858, 60] (* Paolo Xausa, Aug 13 2025 *)

Prog

(Python)
def A386858(n): return 5*n**2>>3

Crossrefs

Cf. A032526, A028895.

Sequence in context: A125622 A080551 A179207 * A008822 A267454 A013927

Adjacent sequences: A386855 A386856 A386857 * A386859 A386860 A386861

Keyword

nonn,easy

Author

Chai Wah Wu, Aug 05 2025

Status

approved