A161731 Expansion of (1-3*x)/(1-8*x+14*x^2).

1, 5, 26, 138, 740, 3988, 21544, 116520, 630544, 3413072, 18476960, 100032672, 541583936, 2932214080, 15875537536, 85953303168, 465368899840, 2519604954368, 13641675037184, 73858930936320, 399887996969984

Offset

0,2

Comments

Fourth binomial transform of A016116.

Inverse binomial transform of A161734. Binomial transform of A086351. - R. J. Mathar, Jun 18 2009

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-14).

Formula

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

a(n) = 8*a(n-1)-14*a(n-2). - R. J. Mathar, Jun 18 2009

a(n) = A081180(n+1) -3*A081180(n). - R. J. Mathar, Jul 19 2012

Mathematica

CoefficientList[Series[(1-3x)/(1-8x+14x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -14}, {1, 5}, 30] (* Harvey P. Dale, Feb 29 2024 *)

Prog

(PARI) F=nfinit(x^2-2); for(n=0, 20, print1(nfeltdiv(F, ((2+x)*(4+x)^n+(2-x)*(4-x)^n), 4)[1], ", ")) \\ Klaus Brockhaus, Jun 19 2009
(Magma)[Floor(((2+Sqrt(2))*(4+Sqrt(2))^n+(2-Sqrt(2))*(4-Sqrt(2))^n)/4): n in [0..30]]; // Vincenzo Librandi, Aug 18 2011

Crossrefs

Cf. A016116, A086351, A161734.

Sequence in context: A083331 A076025 A288785 * A049607 A035029 A081569

Adjacent sequences: A161728 A161729 A161730 * A161732 A161733 A161734

Keyword

nonn,easy

Author

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

Extensions

Extended by R. J. Mathar and Klaus Brockhaus, Jun 18 2009

Edited by Klaus Brockhaus, Jul 05 2009

Status

approved