A103771 Expansion of 1/(1-4x-4x^2-4x^3).

1, 4, 20, 100, 496, 2464, 12240, 60800, 302016, 1500224, 7452160, 37017600, 183879936, 913398784, 4537185280, 22537856000, 111953760256, 556115206144, 2762427289600, 13721985024000, 68162110078976, 338586089570304

Offset

0,2

Comments

The sequence with g.f. 1/(1-r*x-r*x^2-r*x^3) has general term Sum_{k=0..n} T(n-k,k)r^(n-k).

Links

Michael De Vlieger, Table of n, a(n) for n = 0..1436

Yassine Otmani, The 2-Pascal Triangle and a Related Riordan Array, J. Int. Seq. (2025) Vol. 28, Issue 3, Art. No. 25.3.5. See p. 19.

Index entries for linear recurrences with constant coefficients, signature (4,4,4).

Formula

a(n) = Sum_{k=0..n} T(n-k, k)4^(n-k), where T(n, k) = trinomial coefficients (A027907).

Mathematica

CoefficientList[Series[1/(1 - 4 x - 4 x^2 - 4 x^3), {x, 0, 21}], x] (* Michael De Vlieger, May 07 2025 *)

Crossrefs

Cf. A077828, A077835, A000073.

Sequence in context: A098225 A073532 A178874 * A005054 A370536 A216099

Adjacent sequences: A103768 A103769 A103770 * A103772 A103773 A103774

Keyword

easy,nonn

Author

Paul Barry, Feb 15 2005

Status

approved