cp's OEIS Frontend

A249292 Number of length 2+3 0..n arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

%I A249292 #8 Jul 23 2025 11:58:13
%S A249292 26,168,660,2228,5646,12600,25280,46608,80334,131672,206112,311352,
%T A249292 455954,649920,904884,1235024,1654734,2181960,2836016,3638460,4613010,
%U A249292 5786924,7188012,8848968,10803998,13090368,15748356,18822884,22359246
%N A249292 Number of length 2+3 0..n arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.
%C A249292 Row 2 of A249290
%H A249292 R. H. Hardin, <a href="/A249292/b249292.txt">Table of n, a(n) for n = 1..210</a>
%F A249292 Empirical: a(n) = 2*a(n-1) -2*a(n-2) +2*a(n-3) -a(n-4) +a(n-5) -a(n-6) +a(n-8) -2*a(n-9) +a(n-10) -a(n-11) +a(n-12) -2*a(n-13) +2*a(n-14) +2*a(n-18) -2*a(n-19) +a(n-20) -a(n-21) +a(n-22) -2*a(n-23) +a(n-24) -a(n-26) +a(n-27) -a(n-28) +2*a(n-29) -2*a(n-30) +2*a(n-31) -a(n-32)
%F A249292 Also a polynomial of degree 5 plus a linear quasipolynomial with period 360, the first 12 being:
%F A249292 Empirical for n mod 360 = 0: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (107/10)*n
%F A249292 Empirical for n mod 360 = 1: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (967/60)*n - (113/60)
%F A249292 Empirical for n mod 360 = 2: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (481/30)*n + (8/15)
%F A249292 Empirical for n mod 360 = 3: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (49/20)*n - (3/4)
%F A249292 Empirical for n mod 360 = 4: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (641/30)*n - (26/15)
%F A249292 Empirical for n mod 360 = 5: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (647/60)*n - (125/12)
%F A249292 Empirical for n mod 360 = 6: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (107/10)*n - (114/5)
%F A249292 Empirical for n mod 360 = 7: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (787/60)*n - (653/60)
%F A249292 Empirical for n mod 360 = 8: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (481/30)*n - (20/3)
%F A249292 Empirical for n mod 360 = 9: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (109/20)*n + (117/20)
%F A249292 Empirical for n mod 360 = 10: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (641/30)*n + (20/3)
%F A249292 Empirical for n mod 360 = 11: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (467/60)*n + (707/60)
%e A249292 Some solutions for n=10
%e A249292 ..4....0....9....7....5....3....9....2....1....3....3....1....1....5....1....4
%e A249292 ..7....3....7....5....3....2....5....5....5....2....7....7...10....6....6...10
%e A249292 ..4....7....2...10...10....8....6....8....3....1....5...10....1....6....9....3
%e A249292 ..3....1....1....8...10....2....5....9....6...10....3....5....9....6...10....6
%e A249292 ..7....0....0....2....6....8....9....3....7....9....4....7....7....7....5....0
%K A249292 nonn
%O A249292 1,1
%A A249292 _R. H. Hardin_, Oct 24 2014