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A248433 T(n,k)=Number of length n+2 0..k arrays with every three consecutive terms having the sum of some two elements equal to twice the third.

%I A248433 #10 Jul 23 2025 11:41:56
%S A248433 2,9,2,16,9,2,29,20,9,2,42,45,24,9,2,61,70,69,28,9,2,80,105,118,101,
%T A248433 36,9,2,105,140,185,198,165,44,9,2,130,189,252,327,342,261,52,9,2,161,
%U A248433 242,357,462,601,590,389,68,9,2,192,301,470,691,884,1105,1014,645,84,9,2,229,360
%N A248433 T(n,k)=Number of length n+2 0..k arrays with every three consecutive terms having the sum of some two elements equal to twice the third.
%C A248433 Table starts
%C A248433 .2.9..16...29...42....61....80...105...130....161....192....229....266....309
%C A248433 .2.9..20...45...70...105...140...189...242....301....360....437....514....597
%C A248433 .2.9..24...69..118...185...252...357...470....593....716....881...1046...1217
%C A248433 .2.9..28..101..198...327...462...691...932...1203...1474...1829...2184...2551
%C A248433 .2.9..36..165..342...601...884..1381..1922...2533...3144...3957...4770...5613
%C A248433 .2.9..44..261..590..1105..1684..2775..3978...5365...6776...8639..10512..12467
%C A248433 .2.9..52..389.1014..2021..3200..5589..8218..11401..14696..18947..23274..27861
%C A248433 .2.9..68..645.1766..3761..6216.11317.17210..24491..32082..42077..52288..63213
%C A248433 .2.9..84.1029.3062..6969.11944.22921.35962..52505..70120..93459.117518.143619
%C A248433 .2.9.100.1541.5286.12815.22810.46415.74792.112443.153386.207401.264150.326755
%H A248433 R. H. Hardin, <a href="/A248433/b248433.txt">Table of n, a(n) for n = 1..9999</a>
%F A248433 Empirical for column k:
%F A248433 k=1: a(n) = a(n-1)
%F A248433 k=2: a(n) = a(n-1)
%F A248433 k=3: a(n) = a(n-1) +2*a(n-3) -2*a(n-4)
%F A248433 k=4: a(n) = a(n-1) +4*a(n-3) -4*a(n-4)
%F A248433 k=5: a(n) = a(n-1) +6*a(n-3) -6*a(n-4) -4*a(n-6) +4*a(n-7)
%F A248433 k=6: a(n) = 8*a(n-3) -11*a(n-6) +4*a(n-9)
%F A248433 k=7: [order 13]
%F A248433 Empirical for row n:
%F A248433 n=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4); also quadratic polynomial plus a constant quasipolynomial with period 2
%F A248433 n=2: a(n) = a(n-1) +a(n-3) -a(n-5) -a(n-7) +a(n-8); also a quadratic polynomial plus a constant quasipolynomial with period 12
%F A248433 n=3: [order 18; also a quadratic polynomial plus a constant quasipolynomial with period 840]
%F A248433 n=4: [order 36]
%F A248433 n=5: [order 70]
%e A248433 Some solutions for n=6 k=4
%e A248433 ..2....3....3....0....4....3....1....4....0....2....3....0....2....0....2....1
%e A248433 ..4....3....4....2....2....4....3....2....2....4....2....2....0....2....1....0
%e A248433 ..0....3....2....4....0....2....2....3....1....3....1....4....4....1....0....2
%e A248433 ..2....3....3....3....1....3....4....4....0....2....0....0....2....3....2....4
%e A248433 ..1....3....4....2....2....4....3....2....2....1....2....2....0....2....4....0
%e A248433 ..0....3....2....4....0....2....2....3....1....0....4....1....1....4....3....2
%e A248433 ..2....3....0....3....1....0....4....4....0....2....0....3....2....3....2....4
%e A248433 ..1....3....1....2....2....4....0....2....2....4....2....2....0....2....1....3
%K A248433 nonn,tabl
%O A248433 1,1
%A A248433 _R. H. Hardin_, Oct 06 2014