A212537 - OEIS

%I #6 Jun 17 2022 14:21:28

%S 1,3,5,10,12,17,18,23,26,30,31,40,41,43,47,52,53,59,60,67,70,72,73,82,

%T 84,86,89,94,95,103,104,109,111,113,115,125,126,128,130,137,138,144,

%U 145,150,155,157,158,167,168,172,174,179,180,186,188,193,195,197,198,210,211,213

%N Number of nondecreasing sequences of 4 1..n integers with every element dividing the sequence sum.

%C Row 4 of A212536.

%H R. H. Hardin, <a href="/A212537/b212537.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) -2*a(n-2) -a(n-3) +4*a(n-4) -5*a(n-5) +6*a(n-7) -9*a(n-8) +3*a(n-9) +6*a(n-10) -12*a(n-11) +7*a(n-12) +4*a(n-13) -13*a(n-14) +11*a(n-15) -11*a(n-17) +13*a(n-18) -4*a(n-19) -7*a(n-20) +13*a(n-21) -8*a(n-22) -a(n-23) +10*a(n-24) -10*a(n-25) +5*a(n-26) +5*a(n-27) -10*a(n-28) +10*a(n-29) -a(n-30) -8*a(n-31) +13*a(n-32) -7*a(n-33) -4*a(n-34) +13*a(n-35) -11*a(n-36) +11*a(n-38) -13*a(n-39) +4*a(n-40) +7*a(n-41) -12*a(n-42) +6*a(n-43) +3*a(n-44) -9*a(n-45) +6*a(n-46) -5*a(n-48) +4*a(n-49) -a(n-50) -2*a(n-51) +2*a(n-52) -a(n-53).

%e Some solutions for n=8

%e ..4....2....6....7....5....2....1....3....2....1....3....2....4....1....1....1

%e ..4....6....6....7....5....2....2....3....2....2....3....3....6....1....1....1

%e ..8....8....6....7....5....4....3....6....4....2....3....3....6....1....2....4

%e ..8....8....6....7....5....8....6....6....4....5....3....4....8....3....4....6

%Y Cf. A212536.

%K nonn

%O 1,2

%A _R. H. Hardin_, May 20 2012