A011858 - OEIS

%I #49 Oct 01 2022 06:10:22

%S 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,

%T 120,130,140,151,162,174,186,198,211,224,238,252,266,281,296,312,328,

%U 344,361,378,396,414,432,451,470,490,510,530,551,572,594,616,638,661,684

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

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

%H Matthew House, <a href="/A011858/b011858.txt">Table of n, a(n) for n = 0..10000</a>

%H Michael Somos, <a href="https://grail.eecs.csuohio.edu/~somos/somospol.html">Somos Polynomials</a>.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,1).

%F 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

%F Euler transform of length 5 sequence [2, 1, 0, -1, 1]. - _Michael Somos_, Jul 04 2011

%F a(1-n) = a(n). a(n) = a(n-5) + 2*n - 6 for all n in Z. - _Michael Somos_, Jul 04 2011

%F a(n) = a(n-1) + a(n-5) - a(n-6) + 2 for all n in Z. - _Michael Somos_, Jul 06 2011

%F a(n) = (1/5) * ( n^2 - n + [0,0,-2,-1,-2](mod 5) ). - _Ralf Stephan_, Aug 11 2013

%F 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

%F a(n) = A130520(n) + A130520(n+2). - _R. J. Mathar_, Aug 11 2021

%F 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

%e 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 + ...

%e F(5) = y + 1 is of degree a(3) = 1, F(6) = y*z + y + z is of degree a(4) = 2.

%t a[ n_] := Quotient[ n (n - 1), 5]; (* _Michael Somos_, Oct 19 2014 *)

%o (PARI) {a(n) = n * (n - 1) \ 5}; /* _Michael Somos_, Jul 04 2011 */

%o (Magma) [Floor(n*(n-1)/5): n in [0..50]]; // _G. C. Greubel_, Oct 28 2017

%Y Cf. A130520.

%K nonn,easy

%O 0,5

%A _N. J. A. Sloane_