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A246893 Number of length 1+4 0..n arrays with some pair in every consecutive five terms totalling exactly n. 1
30, 231, 900, 2701, 6210, 12931, 23400, 40281, 63750, 97951, 142380, 202981, 278250, 376251, 494160, 642481, 816750, 1030231, 1276500, 1571901, 1907730, 2303731, 2748600, 3265801, 3841110, 4502031, 5231100, 6060181, 6968250, 7991851, 9106080 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).

Conjectures from Colin Barker, Nov 07 2018: (Start)

G.f.: x*(30 + 171*x + 378*x^2 + 619*x^3 + 394*x^4 + 329*x^5 - 2*x^6 + x^7) / ((1 - x)^5*(1 + x)^3).

a(n) = 1 - 5*n + 30*n^2 - 5*n^3 + 10*n^4 for n even.

a(n) = -15 + 20*n + 20*n^2 - 5*n^3 + 10*n^4 for n odd.

(End)

EXAMPLE

Some solutions for n=6:

..5....5....5....4....6....3....4....5....5....3....3....0....3....3....3....1

..1....5....3....1....2....5....1....2....2....3....4....4....0....6....3....6

..3....3....3....2....3....6....5....5....0....6....1....4....1....3....1....5

..2....1....1....2....4....0....0....5....6....0....4....0....5....1....3....2

..3....4....4....1....1....2....6....4....6....0....2....6....4....2....2....2

CROSSREFS

Row 1 of A246892.

Sequence in context: A185032 A291466 A246892 * A190068 A339750 A196412

Adjacent sequences:  A246890 A246891 A246892 * A246894 A246895 A246896

KEYWORD

nonn

AUTHOR

R. H. Hardin, Sep 06 2014

STATUS

approved

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Last modified June 18 12:15 EDT 2021. Contains 345099 sequences. (Running on oeis4.)