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

1, 6, 86, 1366, 21846, 349526, 5592406, 89478486, 1431655766, 22906492246, 366503875926, 5864062014806, 93824992236886, 1501199875790166, 24019198012642646, 384307168202282326, 6148914691236517206, 98382635059784275286, 1574122160956548404566, 25185954575304774473046

Offset

0,2

Comments

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

Binomial transform of A091882.

Links

Table of n, a(n) for n=0..19.

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

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

E.g.f.: (2*exp(x) + exp(16*x))/3. - Amiram Eldar, Feb 01 2026

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 *)

Crossrefs

Cf. A001045, A078008, A091882.

Sequence in context: A318042 A155654 A231165 * A004701 A177570 A343636

Adjacent sequences: A091878 A091879 A091880 * A091882 A091883 A091884

Keyword

easy,nonn

Author

Paul Barry, Feb 10 2004

Status

approved