A151980 Numbers k such that k^2 - k is divisible by 20.

0, 1, 5, 16, 20, 21, 25, 36, 40, 41, 45, 56, 60, 61, 65, 76, 80, 81, 85, 96, 100, 101, 105, 116, 120, 121, 125, 136, 140, 141, 145, 156, 160, 161, 165, 176, 180, 181, 185, 196, 200, 201, 205, 216, 220, 221, 225, 236, 240, 241, 245, 256, 260, 261, 265, 276, 280, 281, 285, 296

Offset

1,3

Links

Table of n, a(n) for n=1..60.

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

Formula

G.f.: x^2*(1+4*x+11*x^2+4*x^3)/((1-x)^2*(1+x)*(1+x^2)). - Colin Barker, Jan 14 2012

a(n) = a(n-1)+a(n-4)-a(n-5). - Colin Barker, Nov 29 2012

a(n) = 10*floor(n/4) + 4*n - 3*floor(n/2) - 4. - Christian Krause, Apr 12 2026

E.g.f.: (8 + 5*cos(x) + (10*x - 13)*cosh(x) + 5*sin(x) + 5*(2*x - 3)*sinh(x))/2. - Stefano Spezia, Apr 13 2026

Mathematica

Select[Range[0, 300], Divisible[#^2-#, 20]&] (* or *) LinearRecurrence[ {1, 0, 0, 1, -1}, {0, 1, 5, 16, 20}, 60] (* Harvey P. Dale, Aug 16 2020 *)

Prog

(Python)
def A151980(n): return 10*(n>>2)-3*(n>>1)+(n-1<<2) # Chai Wah Wu, Apr 13 2026
(PARI) apply( {A151980(n)=n\4*10-n\2*3+n*4-4}, [1..99]) \\ M. F. Hasler, Apr 14 2026

Crossrefs

Sequence in context: A298150 A238586 A195958 * A063612 A269969 A057281

Adjacent sequences: A151977 A151978 A151979 * A151981 A151982 A151983

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 23 2009

Status

approved