cp's OEIS Frontend

A356807 Tetranacci sequence beginning with 3, 7, 12, 24.

%I A356807 #34 Aug 30 2024 09:53:10
%S A356807 3,7,12,24,46,89,171,330,636,1226,2363,4555,8780,16924,32622,62881,
%T A356807 121207,233634,450344,868066,1673251,3225295,6216956,11983568,
%U A356807 23099070,44524889,85824483,165432010,318880452,614661834,1184798779,2283773075,4402114140,8485347828
%N A356807 Tetranacci sequence beginning with 3, 7, 12, 24.
%C A356807 By "Tetranacci sequence" we mean a sequence in which each term is the sum of the four previous terms.
%C A356807 For n>1, a(n) is the number of ways to tile this figure of length n with squares, dominoes, trominoes, and tetraminoes:
%C A356807    ___
%C A356807   |_|_|_________       _
%C A356807   |_|_|_|_|_|_|_| ... |_|
%H A356807 Paolo Xausa, <a href="/A356807/b356807.txt">Table of n, a(n) for n = 1..1000</a>
%H A356807 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1).
%F A356807 a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4).
%F A356807 a(n) = 5*b(n+2) + 2*b(n+1) - 2*b(n-2) for b(n) = A000078(n) the tetranacci numbers.
%F A356807 a(n) = L(n+2) - F(n-2) + Sum_{k=0..n-3} a(k)*F(n-k-1), for L(n) and F(n) the Lucas and Fibonacci numbers.
%F A356807 G.f.: x*(-2*x^3 - 2*x^2 - 4*x - 3)/(x^4 + x^3 + x^2 + x - 1). - _Chai Wah Wu_, Aug 30 2022
%e A356807 Here is one of the a(6) = 89 ways to tile this figure of length 6 with tiles of length <= 4, this one using three squares, one domino, and one tromino:
%e A356807    ___
%e A356807   | |_|_______
%e A356807   |_|_____|_|_|
%t A356807 LinearRecurrence[{1, 1, 1, 1}, {3, 7, 12, 24}, 50] (* _Paolo Xausa_, Aug 30 2024 *)
%Y A356807 Cf. A022120, A100683.
%K A356807 nonn,easy
%O A356807 1,1
%A A356807 _Greg Dresden_ and Hangyu Liang, Aug 29 2022