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A248464 Number of length 3+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third 1
16, 72, 460, 1512, 4272, 9684, 20236, 37868, 67140, 111104, 177024, 269892, 400040, 574140, 806808, 1107132, 1493952, 1978984, 2586340, 3330852, 4242444, 5338788, 6656352, 8217136, 10064140, 12222784, 14744480, 17659176, 21025952, 24879392 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 3 of A248461

LINKS

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

FORMULA

Empirical: a(n) = a(n-1) +a(n-3) -2*a(n-7) +a(n-8) -2*a(n-9) +a(n-10) -a(n-11) +2*a(n-12) +2*a(n-15) -a(n-16) +a(n-17) -2*a(n-18) +a(n-19) -2*a(n-20) +a(n-24) +a(n-26) -a(n-27)

Also a polynomial of degree 5 plus a quadratic quasipolynomial with period 840, the first 12 being:

Empirical for n mod 840 = 0: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (51/5)*n

Empirical for n mod 840 = 1: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (66/5)*n - (33/10)

Empirical for n mod 840 = 2: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (113/15)*n - (152/15)

Empirical for n mod 840 = 3: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (26/5)*n - (1/2)

Empirical for n mod 840 = 4: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (51/5)*n - (12/5)

Empirical for n mod 840 = 5: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (158/15)*n + (1/6)

Empirical for n mod 840 = 6: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (51/5)*n - (24/5)

Empirical for n mod 840 = 7: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (26/5)*n + (67/10)

Empirical for n mod 840 = 8: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (113/15)*n - (4/3)

Empirical for n mod 840 = 9: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (66/5)*n - (9/10)

Empirical for n mod 840 = 10: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (51/5)*n - 8

Empirical for n mod 840 = 11: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (38/15)*n + (41/30)

EXAMPLE

Some solutions for n=6

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

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

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

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

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

CROSSREFS

Sequence in context: A146748 A029872 A056633 * A232572 A098096 A329076

Adjacent sequences: A248461 A248462 A248463 * A248465 A248466 A248467

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 06 2014

STATUS

approved

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Last modified February 5 12:47 EST 2023. Contains 360084 sequences. (Running on oeis4.)