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A255993 Number of length n+2 0..1 arrays with at most one downstep in every n consecutive neighbor pairs. 3
8, 16, 28, 45, 68, 98, 136, 183, 240, 308, 388, 481, 588, 710, 848, 1003, 1176, 1368, 1580, 1813, 2068, 2346, 2648, 2975, 3328, 3708, 4116, 4553, 5020, 5518, 6048, 6611, 7208, 7840, 8508, 9213, 9956, 10738, 11560, 12423, 13328, 14276, 15268, 16305 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 2 of A255992.
Let T(n,k) = n*k + binomial(k+n, n+1), then A001477 (n=0), A000096 (n=1), and presumably this sequence (n=2). Seen this way a(0)=0, a(1)=3 and the offset here should be 2 (as is also hinted by the name: "Number of length n+2 .."). - Peter Luschny, Aug 25 2019
LINKS
FORMULA
Empirical: a(n) = (1/6)*n^3 + n^2 + (23/6)*n + 3.
Empirical g.f.: x*(2 - x)*(4 - 6*x + 3*x^2) / (1 - x)^4. - Colin Barker, Jan 25 2018
Empirical: a(n) = A000292(n+3) - A000124(n+1). - Torlach Rush, Aug 04 2018
EXAMPLE
Some solutions for n=4:
0 0 0 1 0 0 1 1 0 0 1 0 0 1 1 1
0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1
0 1 1 0 0 1 1 0 0 0 1 0 1 0 1 1
0 0 1 0 1 0 1 0 1 1 0 0 1 1 0 1
1 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0
1 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0
CROSSREFS
Cf. A255992.
Sequence in context: A331490 A039288 A045237 * A299644 A204644 A191271
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 13 2015
STATUS
approved

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Last modified April 16 18:22 EDT 2024. Contains 371750 sequences. (Running on oeis4.)