cp's OEIS Frontend

A257062 T(n,k)=Number of length n 1..(k+1) arrays with every leading partial sum divisible by 2 or 3.

%I A257062 #6 Jun 02 2025 11:46:29
%S A257062 1,2,2,3,4,2,3,7,6,2,4,9,18,11,3,4,16,27,45,20,4,5,18,64,81,113,33,4,
%T A257062 6,27,81,256,243,284,59,5,7,35,141,364,1024,729,713,104,7,7,45,200,
%U A257062 738,1636,4096,2187,1791,178,8,8,49,293,1149,3866,7353,16384,6561,4498,314,9
%N A257062 T(n,k)=Number of length n 1..(k+1) arrays with every leading partial sum divisible by 2 or 3.
%C A257062 Table starts
%C A257062 .1...2.....3.....3.......4.......4........5........6.........7.........7
%C A257062 .2...4.....7.....9......16......18.......27.......35........45........49
%C A257062 .2...6....18....27......64......81......141......200.......293.......343
%C A257062 .2..11....45....81.....256.....364......738.....1149......1905......2401
%C A257062 .3..20...113...243....1024....1636.....3866.....6599.....12387.....16807
%C A257062 .4..33...284...729....4096....7353....20249....37893.....80545....117649
%C A257062 .4..59...713..2187...16384...33048...106056...217603....523733....823543
%C A257062 .5.104..1791..6561...65536..148534...555483..1249592...3405505...5764801
%C A257062 .7.178..4498.19683..262144..667585..2909419..7175812..22143847..40353607
%C A257062 .8.314.11297.59049.1048576.3000456.15238479.41207296.143987445.282475249
%H A257062 R. H. Hardin, <a href="/A257062/b257062.txt">Table of n, a(n) for n = 1..9999</a>
%F A257062 Empirical for column k:
%F A257062 k=1: a(n) = a(n-3) +a(n-4)
%F A257062 k=2: a(n) = a(n-2) +3*a(n-3) +a(n-4)
%F A257062 k=3: a(n) = a(n-1) +3*a(n-2) +2*a(n-3)
%F A257062 k=4: a(n) = 3*a(n-1)
%F A257062 k=5: a(n) = 4*a(n-1)
%F A257062 k=6: a(n) = 4*a(n-1) +2*a(n-2) +a(n-3)
%F A257062 k=7: a(n) = 4*a(n-1) +5*a(n-2) +7*a(n-3) +4*a(n-4)
%F A257062 k=8: a(n) = 4*a(n-1) +8*a(n-2) +11*a(n-3) +3*a(n-4)
%F A257062 k=9: a(n) = 5*a(n-1) +9*a(n-2) +5*a(n-3)
%F A257062 k=10: a(n) = 7*a(n-1)
%F A257062 k=11: a(n) = 8*a(n-1)
%F A257062 k=12: a(n) = 8*a(n-1) +4*a(n-2) +2*a(n-3)
%F A257062 k=13: a(n) = 8*a(n-1) +10*a(n-2) +13*a(n-3) +7*a(n-4)
%F A257062 k=14: a(n) = 8*a(n-1) +15*a(n-2) +19*a(n-3) +5*a(n-4)
%F A257062 k=15: a(n) = 9*a(n-1) +15*a(n-2) +8*a(n-3)
%F A257062 k=16: a(n) = 11*a(n-1)
%F A257062 k=17: a(n) = 12*a(n-1)
%F A257062 k=18: a(n) = 12*a(n-1) +6*a(n-2) +3*a(n-3)
%F A257062 k=19: a(n) = 12*a(n-1) +15*a(n-2) +19*a(n-3) +10*a(n-4)
%F A257062 k=20: a(n) = 12*a(n-1) +22*a(n-2) +27*a(n-3) +7*a(n-4)
%F A257062 k=21: a(n) = 13*a(n-1) +21*a(n-2) +11*a(n-3)
%F A257062 k=22: a(n) = 15*a(n-1)
%F A257062 k=23: a(n) = 16*a(n-1)
%F A257062 Empirical for row n:
%F A257062 n=1: a(n) = a(n-1) +a(n-6) -a(n-7)
%F A257062 n=2: a(n) = a(n-1) +2*a(n-6) -2*a(n-7) -a(n-12) +a(n-13)
%F A257062 n=3: a(n) = a(n-1) +3*a(n-6) -3*a(n-7) -3*a(n-12) +3*a(n-13) +a(n-18) -a(n-19)
%F A257062 n=4: [order 25]
%F A257062 n=5: [order 29]
%F A257062 n=6: [order 37]
%F A257062 n=7: [order 43]
%F A257062 Empirical quasipolynomials for row n:
%F A257062 n=1: polynomial of degree 1 plus a quasipolynomial of degree 0 with period 6
%F A257062 n=2: polynomial of degree 2 plus a quasipolynomial of degree 1 with period 6
%F A257062 n=3: polynomial of degree 3 plus a quasipolynomial of degree 2 with period 6
%F A257062 n=4: polynomial of degree 4 plus a quasipolynomial of degree 3 with period 6
%F A257062 n=5: polynomial of degree 5 plus a quasipolynomial of degree 4 with period 6
%F A257062 n=6: polynomial of degree 6 plus a quasipolynomial of degree 5 with period 6
%F A257062 n=7: polynomial of degree 7 plus a quasipolynomial of degree 6 with period 6
%e A257062 Some solutions for n=4 k=4
%e A257062 ..2....2....2....4....4....4....4....2....3....2....3....3....3....4....4....3
%e A257062 ..4....2....4....5....2....5....2....2....3....2....5....5....3....4....2....3
%e A257062 ..4....4....4....1....3....5....2....2....4....5....1....2....2....2....2....3
%e A257062 ..2....1....4....2....5....4....1....4....2....5....5....4....1....5....4....5
%Y A257062 Column 1 is A079398(n+4)
%Y A257062 Column 2 is A026385(n+1)
%Y A257062 Column 4 is A000244
%Y A257062 Column 5 is A000302
%K A257062 nonn,tabl
%O A257062 1,2
%A A257062 _R. H. Hardin_, Apr 15 2015