OFFSET
0,7
COMMENTS
Coefficients in the unique expansion of e/4 = Sum_{n>=1} a(n)/n!, where a(n) satisfies 0<=a(n)<n-1.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,-3,4,-3,2,-1).
FORMULA
a(n)=0 if n=4k, a(n)=k if n=4k+1, a(n)=2k+1 if n=4k+2 and a(n)=k+1 if n=4k+3.
a(n) = floor(n!*e/4) - n*floor((n-1)!*e/4). - Benoit Cloitre, Dec 07 2002
a(n) = Sum_{k=0..n} if(mod(k*n, 4)=2, 1, 0). - Paul Barry, Sep 10 2003
O.g.f.: x^2*(1-x+x^2)/((x-1)^2*(1+x^2)^2). - R. J. Mathar, Jun 13 2008
From Wesley Ivan Hurt, May 30 2015: (Start)
a(n) = 2*a(n-1)-3*a(n-2)+4*a(n-3)-3*a(n-4)+2*a(n-5)-a(n-6), n>6.
a(n) = (-1)^((1-2*n-(-1)^n)/4)*((-1)^n-2*n*(-1)^((2*n+3+(-1)^n)/4)+n*(-1)^((1+(-1)^n)/2)+n*(-1)^((2*n+1+(-1)^n)/2)-1)/8. (End)
EXAMPLE
a(6) = #{1, 3, 5} = 3.
MATHEMATICA
a = Table[0, {i, 1, 50}]; x = Exp[1]/4; For[n = 2, n <= 51, n++, { an = 0; While [(x >= (1/n!)) && (an < (n - 1)), {an++, x = x - (1/n!)} ]}; a[[n - 1]] = an; ]; a
LinearRecurrence[{2, -3, 4, -3, 2, -1}, {0, 0, 1, 1, 0, 1}, 90] (* Harvey P. Dale, Apr 07 2025 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
John W. Layman, Dec 03 2002
EXTENSIONS
More terms from Benoit Cloitre, Dec 07 2002
STATUS
approved