OFFSET
1,3
COMMENTS
Numbers x which are not a solution to 3^x - 2^x == 5 mod 7. - Cino Hilliard, May 14 2003
LINKS
Guenther Schrack, Table of n, a(n) for n = 1..10006
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
G.f.: x^2*(1+3*x+x^2+x^3) / ((1+x)*(1+x^2)*(1-x)^2). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, May 21 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (6*n - 5 - i^(2*n) + (1-i)*i^(-n) + (1+i)*i^n)/4 where i=sqrt(-1).
From Guenther Schrack, Feb 13 2019: (Start)
a(n) = (6*n - 5 - (-1)^n + 2*(-1)^(n*(n + 1)/2))/4.
a(n) = a(n-4) + 6, a(1)=0, a(2)=1, a(3)=4, a(4)=5, for n > 4.
a(-n) = -A047269(n+2). (End)
Sum_{n>=2} (-1)^n/a(n) = sqrt(3)*Pi/36 + log(3)/4 + 2*log(2)/3. - Amiram Eldar, Dec 16 2021
MAPLE
A047260:=n->(6*n-5-I^(2*n)+(1-I)*I^(-n)+(1+I)*I^n)/4: seq(A047260(n), n=1..100); # Wesley Ivan Hurt, May 21 2016
MATHEMATICA
Table[(6n-5-I^(2n)+(1-I)*I^(-n)+(1+I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 21 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 4, 5, 6}, 70] (* Harvey P. Dale, Sep 20 2023 *)
PROG
(Magma) [n : n in [0..100] | n mod 6 in [0, 1, 4, 5]]; // Wesley Ivan Hurt, May 21 2016
(PARI) my(x='x+O('x^70)); concat([0], Vec(x^2*(1+3*x+x^2+x^3)/((1-x)*(1-x^4)))) \\ G. C. Greubel, Feb 16 2019
(Sage) a=(x^2*(1+3*x+x^2+x^3)/((1-x)*(1-x^4))).series(x, 72).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Feb 16 2019
(GAP) Filtered([0..100], n->n mod 6 = 0 or n mod 6 = 1 or n mod 6 = 4 or n mod 6 = 5); # Muniru A Asiru, Feb 19 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Wesley Ivan Hurt, May 21 2016
STATUS
approved