A164606 a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 21.

1, 21, 193, 1573, 12449, 97749, 765857, 5996837, 46948801, 367541781, 2877288193, 22524671653, 176332817249, 1380408754389, 10806429650657, 84597347681957, 662264172758401, 5184486816990741, 40586377233014593, 317727496441303333

Offset

0,2

Comments

Binomial transform of A164605. Fifth binomial transform of A164702.

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) = 21.

a(n) = ((1+4*sqrt(2))*(5+2*sqrt(2))^n + (1-4*sqrt(2))*(5-2*sqrt(2))^n)/2.

G.f.: (1+11*x)/(1-10*x+17*x^2).

E.g.f.: exp(5*x)*(cosh(2*sqrt(2)*x) + 4*sqrt(2)*sinh(2*sqrt(2)*x)). - G. C. Greubel, Aug 10 2017

Mathematica

LinearRecurrence[{10, -17}, {1, 21}, 30] (* Harvey P. Dale, May 22 2013 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+4*r)*(5+2*r)^n+(1-4*r)*(5-2*r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 23 2009
(PARI) x='x+O('x^50); Vec((1+11*x)/(1-10*x+17*x^2)) \\ G. C. Greubel, Aug 10 2017

Crossrefs

Cf. A164605, A164702.

Sequence in context: A010827 A022713 A163718 * A027780 A108679 A200825

Adjacent sequences: A164603 A164604 A164605 * A164607 A164608 A164609

Keyword

nonn,easy

Author

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

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 23 2009

Status

approved