A164609 a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 13.

1, 13, 113, 909, 7169, 56237, 440497, 3448941, 27000961, 211377613, 1654759793, 12954178509, 101410868609, 793887651437, 6214891748017, 48652827405741, 380875114341121, 2981653077513613, 23341653831337073, 182728435995639309

Offset

0,2

Comments

Binomial transform of A164608. Fifth binomial transform of A164683.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..144 from Vincenzo Librandi)

Index entries for linear recurrences with constant coefficients, signature (10, -17).

Formula

a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 13.

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

G.f.: (1+3*x)/(1-10*x+17*x^2).

E.g.f.: exp(5*x)*(cosh(2*sqrt(2)*x) + 2*sqrt(2)*sinh(2*sqrt(2)*x)). - G. C. Greubel, Aug 10 2017

Mathematica

LinearRecurrence[{10, -17}, {1, 13}, 20] (* Harvey P. Dale, Nov 05 2014 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((2+4*r)*(5+2*r)^n+(2-4*r)*(5-2*r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 22 2009
(PARI) x='x+O('x^50); Vec((1+3*x)/(1-10*x+17*x^2)) \\ G. C. Greubel, Aug 10 2017

Crossrefs

Cf. A164608, A164683.

Sequence in context: A021076 A125376 A048545 * A055430 A126534 A361915

Adjacent sequences: A164606 A164607 A164608 * A164610 A164611 A164612

Keyword

nonn,easy

Author

Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 22 2009

Status

approved