OFFSET
0,2
COMMENTS
Binomial transform of A084134.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-15).
FORMULA
a(n) = (5+sqrt(10))^n/2 + (5-sqrt(10))^n/2.
G.f.: (1-5*x)/(1 - 10*x + 15*x^2).
E.g.f.: exp(5*x)*cosh(sqrt(10)*x).
MATHEMATICA
LinearRecurrence[{10, -15}, {1, 5}, 30] (* Harvey P. Dale, Oct 10 2012 *)
PROG
(PARI) a(n)=if(n<0, 0, polsym(x^2-10*x+15, n)[1+n]/2)
(Magma) [n le 2 select 5^(n-1) else 10*Self(n-1) -15*Self(n-2): n in [1..30]]; // G. C. Greubel, Oct 13 2022
(SageMath)
A084135=BinaryRecurrenceSequence(10, -15, 1, 5)
[A084135(n) for n in range(41)] # G. C. Greubel, Oct 13 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 16 2003
STATUS
approved