OFFSET
1,2
COMMENTS
A Jacobsthal variation.
p - q = sqrt(21); p*q = -3; p + q = 3.
REFERENCES
Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001, p. 471.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (3,3).
FORMULA
a(n) = p^n + q^n, where p = (3 + sqrt(21))/2, q = (3 - sqrt 21)/2.
a(n) = 3*a(n-1) + 3*a(n-2), a(1)=3, a(2)=15. - Philippe Deléham, Nov 19 2008
G.f.: G(0)/x - 2/x, where G(k) = 1 + 1/(1 - x*(7*k-3)/(x*(7*k+4) - 2/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 03 2013
EXAMPLE
a(4) = q^4 + q^4 = 207; p^5 + q^5 = 783, where p = (3 + sqrt(21))/2, q = (3 - sqrt(21))/2.
MATHEMATICA
CoefficientList[Series[3x (1+2x)/(1-3x-3x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, 3}, {0, 3, 15}, 30] (* Harvey P. Dale, Jan 10 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jul 02 2003
EXTENSIONS
Zero prepended by Harvey P. Dale, Jan 10 2021
STATUS
approved