OFFSET
1,2
REFERENCES
N. Elkies, The Klein quartic in number theory, pp. 51-101 of S. Levy, ed., The Eightfold Way, Cambridge Univ. Press, 1999. See p. 77 eq. (3.13), (3.14).
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-7,8,-4).
FORMULA
a(n) = 2^n + 1 - 3*(a^n + b^n), where a, b are roots of X^2 - X + 2 = 0.
From Colin Barker, Aug 01 2013: (Start)
a(n) = 4*a(n-1) - 7*a(n-2) + 8*a(n-3) - 4*a(n-4).
G.f.: 2*x^2*(8*x^2-16*x+7) / ((x-1)*(2*x-1)*(2*x^2-x+1)). (End)
EXAMPLE
G.f. = 14*x^2 + 24*x^3 + 14*x^4 + 38*x^6 + 168*x^7 + 350*x^8 + 528*x^9 + ...
MATHEMATICA
LinearRecurrence[{4, -7, 8, -4}, {0, 14, 24, 14}, 40] (* Harvey P. Dale, May 09 2017 *)
PROG
(PARI) {a(n) = if( n<1, 0, 2^n + 1 - 3 * polsym(x^2 - x + 2, n)[n+1])}; /* Michael Somos, Nov 09 2014 */
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved