A011858 a(n) = floor( n*(n-1)/5 ).

0, 0, 0, 1, 2, 4, 6, 8, 11, 14, 18, 22, 26, 31, 36, 42, 48, 54, 61, 68, 76, 84, 92, 101, 110, 120, 130, 140, 151, 162, 174, 186, 198, 211, 224, 238, 252, 266, 281, 296, 312, 328, 344, 361, 378, 396, 414, 432, 451, 470, 490, 510, 530, 551, 572, 594, 616, 638, 661, 684

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n-2) is the total degree of the irreducible factor F(n) of the n-th Somos polynomial. - Michael Somos, Jul 06 2011

Examples

			G.f. = x^3 + 2*x^4 + 4*x^5 + 6*x^6 + 8*x^7 + 11*x^8 + 14*x^9 + 18*x^10 + 22*x^11 + ...
F(5) = y + 1 is of degree a(3) = 1, F(6) = y*z + y + z is of degree a(4) = 2.
		

Links

• Matthew House, Table of n, a(n) for n = 0..10000
• Michael Somos, Somos Polynomials.
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1).

Crossrefs

Cf. A130520.

Programs

Magma

[Floor(n*(n-1)/5): n in [0..50]]; // G. C. Greubel, Oct 28 2017

Mathematica

a[ n_] := Quotient[ n (n - 1), 5]; (* Michael Somos, Oct 19 2014 *)
LinearRecurrence[{2,-1,0,0,1,-2,1},{0,0,0,1,2,4,6},60] (* Harvey P. Dale, Dec 21 2024 *)

PARI

{a(n) = n * (n - 1) \ 5}; /* Michael Somos, Jul 04 2011 */

Formula

G.f.: x^3*(x^2+1)/ ((1-x)^3 * (1+x+x^2+x^3+x^4)). a(n) = +2*a(n-1) -a(n-2) +a(n-5) -2*a(n-6) +a(n-7). - R. J. Mathar, Apr 15 2010

Euler transform of length 5 sequence [2, 1, 0, -1, 1]. - Michael Somos, Jul 04 2011

a(1-n) = a(n). a(n) = a(n-5) + 2*n - 6 for all n in Z. - Michael Somos, Jul 04 2011

a(n) = a(n-1) + a(n-5) - a(n-6) + 2 for all n in Z. - Michael Somos, Jul 06 2011

a(n) = (1/5) * ( n^2 - n + [0,0,-2,-1,-2](mod 5) ). - Ralf Stephan, Aug 11 2013

a(n) - 2*a(n+1) + a(n+2) = (n == 1 (mod 5)) + (n == 3 (mod 5)) for all n in Z. - Michael Somos, Oct 19 2014

a(n) = A130520(n) + A130520(n+2). - R. J. Mathar, Aug 11 2021

Sum_{n>=3} 1/a(n) = 50/9 - sqrt(2*(5+sqrt(5)))*Pi/3 + tan(Pi/(2*sqrt(5)))*Pi/sqrt(5). - Amiram Eldar, Oct 01 2022