cp's OEIS Frontend

A252177 T(n,k)=Number of length n+2 0..k arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

%I A252177 #6 Jul 23 2025 13:37:32
%S A252177 2,3,12,4,49,12,5,132,83,40,6,285,264,369,56,7,536,687,1872,957,144,8,
%T A252177 917,1428,6361,6820,3217,240,9,1464,2729,17092,30315,31420,9295,544,
%U A252177 10,2217,4680,39109,100894,179225,123826,28977,992,11,3220,7661,79672
%N A252177 T(n,k)=Number of length n+2 0..k arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.
%C A252177 Table starts
%C A252177 ....2......3.......4.........5..........6..........7...........8............9
%C A252177 ...12.....49.....132.......285........536........917........1464.........2217
%C A252177 ...12.....83.....264.......687.......1428.......2729........4680.........7661
%C A252177 ...40....369....1872......6361......17092......39109.......79672.......148673
%C A252177 ...56....957....6820.....30315.....100894.....277101......654644......1397115
%C A252177 ..144...3217...31420....179225.....753200....2485637.....6994984.....17238485
%C A252177 ..240...9295..123826....907249....4652710...18231947....59838132....169267931
%C A252177 ..544..28977..515268...4728833...29364176..135424961...513937352...1653595049
%C A252177 ..992..86267.2058802..23847033..177955614..963247737..4190189694..15244143115
%C A252177 .2112.262541.8332796.120644221.1080135428.6838373877.34020988396.139530739057
%H A252177 R. H. Hardin, <a href="/A252177/b252177.txt">Table of n, a(n) for n = 1..181</a>
%F A252177 Empirical for column k:
%F A252177 k=1: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3)
%F A252177 k=2: [order 14]
%F A252177 k=3: [order 39] for n>40
%F A252177 Empirical for row n:
%F A252177 n=1: a(n) = n + 1
%F A252177 n=2: a(n) = (1/6)*n^4 + (7/3)*n^3 + (29/6)*n^2 + (11/3)*n + 1
%F A252177 n=3: a(n) = 3*a(n-1) -8*a(n-3) +6*a(n-4) +6*a(n-5) -8*a(n-6) +3*a(n-8) -a(n-9); also a polynomial of degree 5 plus a quasipolynomial of degree 2 with period 2
%F A252177 n=4: [linear recurrence of order 23; also a polynomial of degree 6 plus a quasipolynomial of degree 3 with period 12]
%e A252177 Some solutions for n=5 k=4
%e A252177 ..0....0....2....1....1....1....1....3....3....2....2....2....1....3....0....4
%e A252177 ..3....2....1....2....0....1....0....4....4....3....2....2....3....0....2....2
%e A252177 ..3....3....4....3....2....2....1....1....4....3....3....4....2....2....3....3
%e A252177 ..3....0....0....3....4....2....0....3....4....2....1....3....2....4....4....4
%e A252177 ..0....1....3....0....1....3....1....1....1....4....0....2....2....3....2....0
%e A252177 ..0....2....1....3....2....3....3....2....1....0....2....3....4....0....2....4
%e A252177 ..3....2....2....1....3....1....1....0....2....1....4....2....1....0....1....0
%Y A252177 Column 1 is A251421
%K A252177 nonn,tabl
%O A252177 1,1
%A A252177 _R. H. Hardin_, Dec 15 2014