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A249290 T(n,k) = Number of length n+3 0..k arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

%I A249290 #8 May 08 2023 07:31:00
%S A249290 14,66,26,204,168,48,524,660,428,88,1098,2228,2144,1094,162,2070,5646,
%T A249290 9504,6960,2792,298,3584,12600,29100,40588,22572,7132,548,5808,25280,
%U A249290 76856,150112,173368,73204,18232,1008,8934,46608,178644,469072,774542
%N A249290 T(n,k) = Number of length n+3 0..k arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.
%C A249290 Table starts
%C A249290 ...14.....66.....204.......524.......1098........2070.........3584.........5808
%C A249290 ...26....168.....660......2228.......5646.......12600........25280........46608
%C A249290 ...48....428....2144......9504......29100.......76856.......178644.......374540
%C A249290 ...88...1094....6960.....40588.....150112......469072......1263044......3011088
%C A249290 ..162...2792...22572....173368.....774542.....2863158......8930228.....24208540
%C A249290 ..298...7132...73204....740616....3996816....17477172.....63142432....194636612
%C A249290 ..548..18232..237480...3164312...20626236...106687006....446465388...1564897170
%C A249290 .1008..46616..770416..13520668..106449362...651265876...3156873140..12581992958
%C A249290 .1854.119176.2499164..57772560..549377682..3975630136..22321652802.101161030608
%C A249290 .3410.304696.8107012.246857788.2835311880.24269116850.157832259724.813349549954
%H A249290 R. H. Hardin, <a href="/A249290/b249290.txt">Table of n, a(n) for n = 1..9999</a>
%F A249290 Empirical for column k:
%F A249290 k=1: a(n) = a(n-1) +a(n-2) +a(n-3)
%F A249290 k=2: [order 12]
%F A249290 k=3: [order 8]
%F A249290 k=4: [order 40]
%F A249290 k=5: [order 87]
%F A249290 Empirical for row n:
%F A249290 n=1: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +a(n-5) +2*a(n-6) -3*a(n-7) +a(n-8); also a polynomial of degree 4 plus a constant quasipolynomial with period 6
%F A249290 n=2: [order 32; also a polynomial of degree 5 plus a linear quasipolynomial with period 360]
%e A249290 Some solutions for n=4, k=4
%e A249290 ..3....4....1....4....3....0....4....2....3....1....1....3....0....0....3....1
%e A249290 ..2....0....4....1....2....1....4....3....0....1....0....2....3....2....2....0
%e A249290 ..0....3....0....1....4....4....2....3....4....0....4....0....0....0....4....4
%e A249290 ..2....3....4....4....4....1....3....2....4....0....3....2....4....0....0....4
%e A249290 ..1....1....3....0....1....4....0....1....2....4....3....2....0....2....4....3
%e A249290 ..0....4....2....4....4....4....1....4....0....1....3....0....1....1....0....0
%e A249290 ..3....0....2....0....2....4....4....4....0....4....4....2....0....2....0....0
%Y A249290 Column 1 is A135491(n+3).
%K A249290 nonn,tabl
%O A249290 1,1
%A A249290 _R. H. Hardin_, Oct 24 2014