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A161731
Expansion of (1-3*x)/(1-8*x+14*x^2).
6
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
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
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