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
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).
Programs
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Mathematica
CoefficientList[Series[1/(1 - 4 x - 4 x^2 - 4 x^3), {x, 0, 21}], x] (* Michael De Vlieger, May 07 2025 *)
Formula
a(n) = Sum_{k=0..n} T(n-k, k)4^(n-k), where T(n, k) = trinomial coefficients (A027907).
Comments