A241615 Number of length n+2 0..9 arrays with no consecutive three elements summing to more than 9.

220, 1210, 6655, 34243, 180829, 963886, 5093737, 26932543, 142701909, 755538278, 3999038946, 21172904049, 112098384491, 593455432350, 3141868198978, 16633824615067, 88062718713584, 466221475528171, 2468274573927916

Offset: 1

Author

R. H. Hardin, Apr 26 2014

Keywords

• nonn

Comments

Column 9 of A241619

Examples

			Some solutions for n=5
..0....1....0....1....1....7....5....5....1....0....0....1....1....1....1....0
..5....2....1....2....1....0....1....1....3....1....1....2....2....0....7....1
..2....1....3....1....2....0....0....3....1....2....2....4....1....0....1....7
..0....3....1....5....0....4....1....2....2....5....3....3....1....0....0....0
..3....1....0....0....0....0....3....0....4....0....2....0....5....1....4....1
..2....4....8....1....1....3....0....4....0....1....2....3....1....8....1....3
..3....1....1....1....2....3....6....5....4....2....4....4....0....0....2....4
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Robert Israel, Maple-assisted proof of empirical formula

Programs

Maple

r:= [seq(seq([i,j],j=0..9-i),i=0..9)]:
T:= Matrix(55,55,proc(i,j) if r[i][1]=r[j][2] and r[i][1]+r[i][2]+r[j][1]<=9 then 1 else 0 fi end proc):
U[0]:= Vector(55,1):
for n from 1 to 50 do U[n]:= T . U[n-1] od:
seq(U[0]^%T . U[j], j=1..50); # Robert Israel, Sep 03 2019

Formula

Empirical: a(n) = 4*a(n-1) +2*a(n-2) +44*a(n-3) -69*a(n-4) -79*a(n-5) -507*a(n-6) +572*a(n-7) +514*a(n-8) +2973*a(n-9) -3097*a(n-10) -1820*a(n-11) -10364*a(n-12) +10800*a(n-13) +4269*a(n-14) +25019*a(n-15) -25821*a(n-16) -6914*a(n-17) -44207*a(n-18) +44275*a(n-19) +8829*a(n-20) +59359*a(n-21) -57787*a(n-22) -9308*a(n-23) -62456*a(n-24) +58989*a(n-25) +8291*a(n-26) +52174*a(n-27) -48385*a(n-28) -5846*a(n-29) -35493*a(n-30) +32403*a(n-31) +3452*a(n-32) +19719*a(n-33) -17810*a(n-34) -1563*a(n-35) -9053*a(n-36) +8178*a(n-37) +608*a(n-38) +3390*a(n-39) -3025*a(n-40) -167*a(n-41) -1072*a(n-42) +973*a(n-43) +42*a(n-44) +259*a(n-45) -227*a(n-46) -6*a(n-47) -56*a(n-48) +52*a(n-49) +a(n-50) +7*a(n-51) -6*a(n-52) -a(n-54) +a(n-55).

Empirical formula verified: see link. - Robert Israel, Sep 03 2019