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

Author

Paul Barry, May 16 2003

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A084134.

Programs

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

Mathematica

LinearRecurrence[{10,-15},{1,5},30] (* Harvey P. Dale, Oct 10 2012 *)

PARI

a(n)=if(n<0,0,polsym(x^2-10*x+15,n)[1+n]/2)

SageMath

A084135=BinaryRecurrenceSequence(10,-15,1,5)
[A084135(n) for n in range(41)] # G. C. Greubel, Oct 13 2022

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).