A163346 a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 7.

1, 7, 47, 309, 2009, 12983, 83623, 537621, 3452881, 22163527, 142219007, 912428949, 5853252329, 37546657463, 240841771063, 1544844588981, 9909085155361, 63559426007047, 407685301497167, 2614986216809589, 16773100233661049, 107586319349989943

Offset

0,2

Comments

Binomial transform of A163350. Fifth binomial transform of A163403.

Links

Matthew House, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-23).

Formula

a(n) = 10*a(n-1)-23*a(n-2) for n > 1; a(0) = 1, a(1) = 7.

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

G.f.: (1-3*x)/(1-10*x+23*x^2).

E.g.f.: (sqrt(2)*sinh(sqrt(2)*x) + cosh(sqrt(2)*x))*exp(5*x). - Ilya Gutkovskiy, Jun 30 2016

Mathematica

CoefficientList[Series[(1 - 3 x)/(1 - 10 x + 23 x^2), {x, 0, 21}], x] (* Michael De Vlieger, Jun 30 2016 *)
LinearRecurrence[{10, -23}, {1, 7}, 50] (* G. C. Greubel, Dec 19 2016 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+r)*(5+r)^n+(1-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 26 2009
(PARI) Vec((1-3*x)/(1-10*x+23*x^2) + O(x^99)) \\ Altug Alkan, Jul 05 2016

Crossrefs

Cf. A163350, A163403.

Sequence in context: A126635 A085352 A125370 * A186446 A244830 A126528

Adjacent sequences: A163343 A163344 A163345 * A163347 A163348 A163349

Keyword

nonn,easy

Author

Al Hakanson (hawkuu(AT)gmail.com), Jul 25 2009

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 26 2009

New name from G. C. Greubel, Dec 19 2016

Status

approved