A164538 a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 5, a(1) = 33.

5, 33, 215, 1391, 8965, 57657, 370375, 2377639, 15257765, 97891953, 627990935, 4028394431, 25840152805, 165748456137, 1063161046855, 6819395977399, 43741255696325, 280566449483073, 1799615613815255, 11543127800041871

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A164537. Fifth binomial transform of A164682.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..151
• Index entries for linear recurrences with constant coefficients, signature (10,-23).

Crossrefs

Cf. A164537, A164682.

Programs

Magma

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((5+4*r)*(5+r)^n+(5-4*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 21 2009

Mathematica

LinearRecurrence[{10,-23},{5,33},20] (* Harvey P. Dale, May 29 2019 *)

PARI

Vec((5-17*x)/(1-10*x+23*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jun 14 2011

Formula

a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 5, a(1) = 33.

G.f.: (5-17*x)/(1-10*x+23*x^2).

a(n) = ((5+4*sqrt(2))*(5+sqrt(2))^n + (5-4*sqrt(2))*(5-sqrt(2))^n)/2.

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 21 2009