cp's OEIS Frontend

A190041 T(n,k)=Number of nondecreasing arrangements of n+2 numbers in 0..k with the last equal to k and each after the second equal to the sum of one or two of the preceding three.

%I A190041 #7 Jul 22 2025 11:59:21
%S A190041 2,4,2,5,6,2,7,7,8,2,8,12,10,10,2,10,12,18,14,12,2,11,18,16,27,18,14,
%T A190041 2,13,17,30,23,39,22,16,2,14,24,22,47,33,53,26,18,2,16,22,40,31,72,45,
%U A190041 69,30,20,2,17,30,31,65,43,107,57,87,34,22,2,19,27,49,49,105,60,151,69,107
%N A190041 T(n,k)=Number of nondecreasing arrangements of n+2 numbers in 0..k with the last equal to k and each after the second equal to the sum of one or two of the preceding three.
%C A190041 Table starts
%C A190041 .2..4..5...7..8..10..11..13..14..16..17...19..20...22...23...25..26...28..29
%C A190041 .2..6..7..12.12..18..17..24..22..30..27...36..32...42...37...48..42...54..47
%C A190041 .2..8.10..18.16..30..22..40..31..49..36...64..41...71...53...81..55...97..61
%C A190041 .2.10.14..27.23..47..31..65..49..76..52..113..58..109...92..132..78..167..87
%C A190041 .2.12.18..39.33..72..43.105..69.123..72..190..83..169..151..217.108..276.120
%C A190041 .2.14.22..53.45.107..60.164.100.189..99..311.121..251..241..358.146..447.167
%C A190041 .2.16.26..69.57.151..80.246.144.284.138..492.178..372..364..583.195..717.239
%C A190041 .2.18.30..87.69.203.100.349.200.409.189..754.258..545..540..927.267.1109.341
%C A190041 .2.20.34.107.81.263.120.472.264.560.245.1108.352..775..778.1424.364.1677.484
%C A190041 .2.22.38.129.93.331.140.617.336.735.301.1561.448.1053.1072.2094.474.2449.657
%H A190041 R. H. Hardin, <a href="/A190041/b190041.txt">Table of n, a(n) for n = 1..4434</a>
%F A190041 Empirical: T(n,1) = 2
%F A190041 Empirical: T(n,2) = 2*n + 2
%F A190041 Empirical: T(n,3) = 4*n - 2 for n>2
%F A190041 Empirical: T(n,4) = n^2 + 3*n - 1 for n>3
%F A190041 Empirical: T(n,5) = 12*n - 27 for n>4
%F A190041 Empirical: T(n,6) = 4*n^2 - 8*n + 11 for n>5
%F A190041 Empirical: T(n,7) = 20*n - 60 for n>5
%F A190041 Empirical: T(n,8) = (1/3)*n^3 + 2*n^2 + (50/3)*n - 83 for n>6
%e A190041 Some solutions for n=5 k=3
%e A190041 ..2....3....1....1....0....1....0....0....0....0....1....1....1....1....1....1
%e A190041 ..3....3....1....1....1....2....1....1....1....3....1....3....1....1....1....2
%e A190041 ..3....3....2....1....1....3....1....1....1....3....1....3....1....1....2....2
%e A190041 ..3....3....3....1....1....3....2....1....2....3....1....3....1....2....2....3
%e A190041 ..3....3....3....2....1....3....3....2....2....3....1....3....2....3....3....3
%e A190041 ..3....3....3....3....2....3....3....3....3....3....2....3....2....3....3....3
%e A190041 ..3....3....3....3....3....3....3....3....3....3....3....3....3....3....3....3
%Y A190041 Row 1 is A001651(n+1)
%Y A190041 Row 2 is A189327
%K A190041 nonn,tabl
%O A190041 1,1
%A A190041 _R. H. Hardin_ May 04 2011