cp's OEIS Frontend

A248435 Number of length 2+2 0..n arrays with every three consecutive terms having the sum of some two elements equal to twice the third.

%I A248435 #7 Nov 08 2018 08:53:34
%S A248435 2,9,20,45,70,105,140,189,242,301,360,437,514,597,684,785,886,997,
%T A248435 1108,1233,1362,1497,1632,1785,1938,2097,2260,2437,2614,2801,2988,
%U A248435 3189,3394,3605,3816,4045,4274,4509,4748,5001,5254,5517,5780,6057,6338,6625,6912
%N A248435 Number of length 2+2 0..n arrays with every three consecutive terms having the sum of some two elements equal to twice the third.
%H A248435 R. H. Hardin, <a href="/A248435/b248435.txt">Table of n, a(n) for n = 1..210</a>
%F A248435 Empirical: a(n) = a(n-1) + a(n-3) - a(n-5) - a(n-7) + a(n-8).
%F A248435 Empirical for n mod 12 = 0: a(n) = (19/6)*n^2 - (5/3)*n + 1
%F A248435 Empirical for n mod 12 = 1: a(n) = (19/6)*n^2 - (5/3)*n + (1/2)
%F A248435 Empirical for n mod 12 = 2: a(n) = (19/6)*n^2 - (5/3)*n - (1/3)
%F A248435 Empirical for n mod 12 = 3: a(n) = (19/6)*n^2 - (5/3)*n - (7/2)
%F A248435 Empirical for n mod 12 = 4: a(n) = (19/6)*n^2 - (5/3)*n + 1
%F A248435 Empirical for n mod 12 = 5: a(n) = (19/6)*n^2 - (5/3)*n - (5/6)
%F A248435 Empirical for n mod 12 = 6: a(n) = (19/6)*n^2 - (5/3)*n + 1
%F A248435 Empirical for n mod 12 = 7: a(n) = (19/6)*n^2 - (5/3)*n - (7/2)
%F A248435 Empirical for n mod 12 = 8: a(n) = (19/6)*n^2 - (5/3)*n - (1/3)
%F A248435 Empirical for n mod 12 = 9: a(n) = (19/6)*n^2 - (5/3)*n + (1/2)
%F A248435 Empirical for n mod 12 = 10: a(n) = (19/6)*n^2 - (5/3)*n + 1
%F A248435 Empirical for n mod 12 = 11: a(n) = (19/6)*n^2 - (5/3)*n - (29/6).
%F A248435 Empirical g.f.: x*(2 + 7*x + 11*x^2 + 23*x^3 + 16*x^4 + 17*x^5 - x^6 + x^7) / ((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x + x^2)). - _Colin Barker_, Nov 08 2018
%e A248435 Some solutions for n=6:
%e A248435 ..4....4....6....4....3....5....3....4....2....0....0....2....3....1....3....6
%e A248435 ..3....3....2....6....2....1....5....0....1....2....3....3....5....2....1....0
%e A248435 ..5....2....4....2....4....3....4....2....3....1....6....4....1....0....2....3
%e A248435 ..4....4....0....4....6....5....6....1....5....0....0....2....3....4....3....6
%Y A248435 Row 2 of A248433.
%K A248435 nonn
%O A248435 1,1
%A A248435 _R. H. Hardin_, Oct 06 2014