A164543 a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 17.

1, 17, 153, 1241, 9809, 76993, 603177, 4722889, 36974881, 289459697, 2266023993, 17739425081, 138871842929, 1087148202913, 8510660699337, 66625087543849, 521569643549761, 4083069947252177, 31964015532175833, 250227966218471321

Offset

0,2

Comments

Binomial transform of A164542. Fifth binomial transform of A164675.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..144

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) = 17.

G.f.: (1+7*x)/(1-10*x+17*x^2).

a(n) = ((1+3*sqrt(2))*(5+2*sqrt(2))^n + (1-3*sqrt(2))*(5-2*sqrt(2))^n)/2.

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(5+2*r)^n+(1-3*r)*(5-2*r)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 20 2009

Crossrefs

Cf. A164542, A164675.

Sequence in context: A247613 A010969 A022582 * A295932 A298458 A160699

Adjacent sequences: A164540 A164541 A164542 * A164544 A164545 A164546

Keyword

nonn,easy

Author

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

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 20 2009

Status

approved