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A211563 Number of nonnegative integer arrays of length n+3 with new values 0 upwards introduced in order, and containing the value n-1. 1
15, 51, 171, 512, 1345, 3145, 6676, 13091, 24047, 41835, 69525, 111126, 171761, 257857, 377350, 539905, 757151, 1042931, 1413567, 1888140, 2488785, 3241001, 4173976, 5320927, 6719455, 8411915, 10445801, 12874146, 15755937, 19156545 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 4 of A211561.
LINKS
FORMULA
Empirical: a(n) = (1/48)*n^6 + (7/48)*n^5 + (23/48)*n^4 + (61/48)*n^3 + 3*n^2 + (61/12)*n + 5.
Empirical: a(n) = sum{j in n..n+3}stirling2(n+3,j).
Conjectures from Colin Barker, Jul 19 2018: (Start)
G.f.: x*(15 - 54*x + 129*x^2 - 139*x^3 + 92*x^4 - 33*x^5 + 5*x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
EXAMPLE
Some solutions for n=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....0....1....1....1....1....1....1....1....1....1....1....1
..2....2....2....2....1....0....2....2....2....2....2....2....2....2....2....2
..1....3....3....3....2....2....3....3....2....0....3....0....3....1....2....1
..3....4....2....0....3....3....4....0....1....3....4....0....0....1....3....3
..3....5....4....3....4....4....5....4....3....4....4....3....2....0....4....4
..4....6....4....3....1....2....6....2....2....4....5....4....4....3....0....4
..1....1....1....4....5....1....7....0....4....0....5....4....1....4....3....1
CROSSREFS
Cf. A211561.
Sequence in context: A044008 A201054 A009962 * A214522 A118238 A015234
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 15 2012
STATUS
approved

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Last modified May 22 19:06 EDT 2024. Contains 372758 sequences. (Running on oeis4.)