A151973 Numbers n such that n^2 - n is divisible by 24.
0, 1, 9, 16, 24, 25, 33, 40, 48, 49, 57, 64, 72, 73, 81, 88, 96, 97, 105, 112, 120, 121, 129, 136, 144, 145, 153, 160, 168, 169, 177, 184, 192, 193, 201, 208, 216, 217, 225, 232, 240, 241, 249, 256, 264, 265, 273, 280, 288, 289, 297, 304, 312, 313, 321, 328, 336, 337, 345
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
Programs
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Magma
[n: n in [0..350] | IsZero(n*(n-1) mod 24)]; // Bruno Berselli, Nov 29 2012
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Maple
A151973:=n->(12*n+3*I^(n*(n-1))-2*I^(2*n)-17)/2: seq(A151973(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016
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Mathematica
CoefficientList[Series[x (8 x^3 + 7 x^2 + 8 x + 1) / ((x - 1)^2 (x + 1) (x^2 + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *) -
PARI
is(n)=(n^2-n)%24==0 \\ Charles R Greathouse IV, Oct 16 2015
Formula
a(n) = a(n-1)+a(n-4)-a(n-5) for n>5. G.f.: x^2*(8*x^3+7*x^2+8*x+1) / ((x-1)^2*(x+1)*(x^2+1)). - Colin Barker, Nov 29 2012
a(n) = (12*n+3*i^(n*(n-1))-2*(-1)^n-17)/2, where i=sqrt(-1). - Bruno Berselli, Nov 29 2012