A212537 Number of nondecreasing sequences of 4 1..n integers with every element dividing the sequence sum.

1, 3, 5, 10, 12, 17, 18, 23, 26, 30, 31, 40, 41, 43, 47, 52, 53, 59, 60, 67, 70, 72, 73, 82, 84, 86, 89, 94, 95, 103, 104, 109, 111, 113, 115, 125, 126, 128, 130, 137, 138, 144, 145, 150, 155, 157, 158, 167, 168, 172, 174, 179, 180, 186, 188, 193, 195, 197, 198, 210, 211, 213

Offset

1,2

Comments

Row 4 of A212536.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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).

Example

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

Crossrefs

Cf. A212536.

Sequence in context: A336531 A285415 A275668 * A047389 A263652 A285679

Adjacent sequences: A212534 A212535 A212536 * A212538 A212539 A212540

Keyword

nonn

Author

R. H. Hardin, May 20 2012

Status

approved