%I #6 Dec 26 2023 18:07:17

%S 524,2228,9504,40588,173368,740616,3164312,13520668,57772560,

%T 246857788,1054810472,4507167504,19258980852,82293014888,351635522044,

%U 1502528043892,6420257600360,27433569837528,117222829267252

%N Number of length n+3 0..4 arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

%C Column 4 of A249290.

%H R. H. Hardin, <a href="/A249286/b249286.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +3*a(n-2) +9*a(n-3) +35*a(n-4) -65*a(n-5) -151*a(n-6) -317*a(n-7) -534*a(n-8) -140*a(n-9) +1280*a(n-10) +2126*a(n-11) +2048*a(n-12) +5830*a(n-13) +4946*a(n-14) +11778*a(n-15) +25333*a(n-16) +19483*a(n-17) -11542*a(n-18) -9074*a(n-19) -7639*a(n-20) -13027*a(n-21) +38961*a(n-22) -25267*a(n-23) -187805*a(n-24) -120777*a(n-25) +143132*a(n-26) +88370*a(n-27) -57497*a(n-28) -100517*a(n-29) -152210*a(n-30) -3304*a(n-31) +156512*a(n-32) +254068*a(n-33) +111836*a(n-34) -84272*a(n-35) -31976*a(n-36) +9504*a(n-37) -3632*a(n-38) -144*a(n-39) +576*a(n-40).

%e Some solutions for n=5

%e ..2....0....0....1....1....2....2....1....1....1....0....2....0....0....0....0

%e ..3....4....3....0....1....0....1....2....0....2....2....1....2....3....1....2

%e ..1....4....1....4....2....0....0....1....0....4....0....4....2....2....1....2

%e ..0....0....3....4....3....0....3....3....2....3....0....2....3....1....4....0

%e ..3....4....2....1....3....4....4....0....3....2....1....4....3....4....0....0

%e ..2....0....4....4....1....3....3....4....4....2....4....3....3....2....4....1

%e ..0....3....2....4....4....2....0....0....2....0....4....0....1....2....4....1

%e ..2....2....3....2....1....2....3....1....0....3....1....3....3....1....4....0

%Y Cf. A249290.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 24 2014