A091881 Expansion of (1-11x)/((1-x)(1-16x)).

1, 6, 86, 1366, 21846, 349526, 5592406, 89478486, 1431655766, 22906492246, 366503875926, 5864062014806, 93824992236886, 1501199875790166, 24019198012642646, 384307168202282326, 6148914691236517206

Offset: 0

Author

Paul Barry, Feb 10 2004

Keywords

• easy
• nonn

Comments

With interpolated zeros, this is the multinomial expression sum{i=0..n,sum{j=0..n,sum{k=0..n,if (mod(n-2i-4j-4k,6)=0,n!/(i!j!k!(n-i-j-k)!),0)}}}. Binomial transform of A091882.

Links

• Index entries for linear recurrences with constant coefficients, signature (17,-16).

Crossrefs

Cf. A001045, A078008, A091882.

Programs

Mathematica

CoefficientList[Series[(1-11x)/((1-x)(1-16x)),{x,0,30}],x] (* or *) LinearRecurrence[{17,-16},{1,6},30] (* Harvey P. Dale, Dec 15 2011 *)

Formula

a(n) = 16^n/3 + 2/3; a(n) = A001045(4*n) + 1.

a(0)=1, a(1)=6, a(n) = 17*a(n-1) - 16*a(n-2) [Harvey P. Dale, Dec 15 2011]

a(n) = A078008(4n). - Oboifeng Dira, May 29 2020