A174850 Quintisection A061037(5*n-2).

0, 5, 15, 165, 20, 525, 195, 1085, 90, 1845, 575, 2805, 210, 3965, 1155, 5325, 380, 6885, 1935, 8645, 600, 10605, 2915, 12765, 870, 15125, 4095, 17685, 1190, 20445, 5475, 23405, 1560, 26565, 7055, 29925, 1980, 33485, 8835, 37245, 2450

Offset: 0

Author

Paul Curtz, Dec 01 2010

Keywords

• nonn
• easy
• frac

Comments

All entries are multiples of 5. Like A061037(n+2), the (2k+1)-sections A061037((2*k+1)*n-2) are multiples of 2k+1; see A165248, A165943.

The sequence contains 4 interlaced second-order polynomials: a(4n) = 5n*(5n-1), a(4n+1) = 5*(4n+1)*(20n+1), a(4n+2)= 5*(2n+1)*(10n+3), a(4n+3)= 5*(4n+3)*(20n+11). - R. J. Mathar, Feb 10 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).

Programs

Magma

[ Numerator(1/4-1/(5*n-2)^2): n in [0..40] ]; // Bruno Berselli, Feb 10 2011

Mathematica

f[n_] := n/GCD[n, 4]; Table[ f[n] f[n + 4], {n, -4, 200, 5}] (* Robert G. Wilson v, Feb 03 2011 *)

PARI

vector(50, n, n--; numerator( 1/4 - 1/(5*n-2)^2 )) \\ G. C. Greubel, Sep 19 2018

Formula

a(n) = numerator( 1/4 - 1/(5*n-2)^2 ).

From R. J. Mathar, Feb 10 2011: (Start)

a(n) = +3*a(n-4) -3*a(n-8) +a(n-12).

G.f. ( -5*x*(1+3*x+33*x^2+4*x^3+102*x^4+30*x^5+118*x^6+6*x^7+57*x^8 +7*x^9+9*x^10) )/( (x-1)^3*(1+x)^3*(x^2+1)^3 ). (End)

a(n) = 5*n*(5*n-4)*(37-27*(-1)^n-3*(-i)^n-3*i^n)/64, where i=sqrt(-1). - Bruno Berselli, Feb 10 2011