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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A016116, A086351, A161734.

Programs

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

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 *)

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

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

Extensions

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

Edited by Klaus Brockhaus, Jul 05 2009