A084135 a(n) = 10*a(n-1) - 15*a(n-2), a(0)=1, a(1)=5.

1, 5, 35, 275, 2225, 18125, 147875, 1206875, 9850625, 80403125, 656271875, 5356671875, 43722640625, 356876328125, 2912923671875, 23776091796875, 194067062890625, 1584029251953125, 12929286576171875, 105532426982421875

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

Cf. A084134.

Sequence in context: A180900 A344840 A087630 * A229111 A138233 A322666

Adjacent sequences: A084132 A084133 A084134 * A084136 A084137 A084138

Keyword

easy,nonn

Author

Paul Barry, May 16 2003

Status

approved