OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,5,-7).
FORMULA
a(n) = ((1+sqrt(8))^n + (1-sqrt(8))^n + 2)/4.
a(n) = (A084058(n) + 1)/2.
E.g.f.: exp(x)*cosh(sqrt(2)*x)^2.
G.f.: (1+x)*(1-3*x) / ( (1-x)*(1-2*x-7*x^2) ). - R. J. Mathar, Nov 09 2012
MATHEMATICA
LinearRecurrence[{3, 5, -7}, {1, 1, 5}, 30] (* Harvey P. Dale, Nov 08 2017 *)
PROG
(PARI) my(x='x+O('x^30)); round(Vec(serlaplace(exp(x)*cosh(sqrt(2)*x)^2))) \\ G. C. Greubel, Sep 11 2018
(Magma) I:=[1, 1, 5]; [n le 3 select I[n] else 3*Self(n-1) +5*Self(n-2) - 7*Self(n-3): n in [1..30]]; // G. C. Greubel, Sep 11 2018
(SageMath)
A084058=BinaryRecurrenceSequence(2, 7, 1, 1)
[A084136(n) for n in range(41)] # G. C. Greubel, Oct 13 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 16 2003
STATUS
approved