A151981 Numbers n such that n^2 - n is divisible by 48.

0, 1, 16, 33, 48, 49, 64, 81, 96, 97, 112, 129, 144, 145, 160, 177, 192, 193, 208, 225, 240, 241, 256, 273, 288, 289, 304, 321, 336, 337, 352, 369, 384, 385, 400, 417, 432, 433, 448, 465, 480, 481, 496, 513, 528, 529, 544, 561, 576, 577, 592, 609, 624, 625, 640, 657, 672

Offset: 1

Author

N. J. A. Sloane, Aug 23 2009

Keywords

• nonn
• easy

Comments

Numbers congruent to {0, 1, 16, 33} mod 48. - Charles R Greathouse IV, Apr 10 2012

Links

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

Programs

Magma

[n : n in [0..800] | n mod 48 in [0, 1, 16, 33]]; // Wesley Ivan Hurt, Jun 07 2016

Maple

A151981:=n->12*n-(35+3*I^(2*n))/2+(2+2*I)*I^(-n)+(2-2*I)*I^n: seq(A151981(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

Mathematica

Table[12n-(35+3*I^(2*n))/2+(2+2*I)*I^(-n)+(2-2*I)*I^n, {n, 80}] (* Wesley Ivan Hurt, Jun 07 2016 *)

PARI

a(n)=n\4*48+[-15, 0, 1, 16][n%4+1] \\ Charles R Greathouse IV, Apr 10 2012

Formula

From Colin Barker, Apr 10 2012: (Start)

G.f.: x^2*(1+15*x+17*x^2+15*x^3)/((1-x)^2*(1+x)*(1+x^2)).

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. (End)

a(n) = 12*n-(35+3*i^(2*n))/2+(2+2*i)*i^(-n)+(2-2*i)*i^n where i=sqrt(-1). - Wesley Ivan Hurt, Jun 07 2016