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A248463 Number of length 2+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third. 1
10, 36, 148, 380, 862, 1652, 2956, 4860, 7642, 11400, 16488, 23044, 31482, 41952, 54956, 70672, 89662, 112128, 138708, 169632, 205610, 246884, 294240, 347960, 408890, 477324, 554196, 639828, 735214, 840700, 957356, 1085556, 1226442 (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) - a(n-3) - 2*a(n-5) + 2*a(n-6) + a(n-8) - 2*a(n-10) + a(n-11).

Empirical for n mod 12 = 0: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n.

Empirical for n mod 12 = 1: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n + (5/2).

Empirical for n mod 12 = 2: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n - (4/3).

Empirical for n mod 12 = 3: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n - (3/2).

Empirical for n mod 12 = 4: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n.

Empirical for n mod 12 = 5: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n + (7/6).

Empirical for n mod 12 = 6: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n.

Empirical for n mod 12 = 7: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n - (3/2).

Empirical for n mod 12 = 8: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n - (4/3).

Empirical for n mod 12 = 9: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n + (5/2).

Empirical for n mod 12 = 10: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n.

Empirical for n mod 12 = 11: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n - (17/6).

Empirical g.f.: 2*x*(5 + 8*x + 38*x^2 + 47*x^3 + 69*x^4 + 48*x^5 + 42*x^6 + 17*x^7 + 14*x^8) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Nov 08 2018

EXAMPLE

Some solutions for n=6:

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

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

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

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

CROSSREFS

Row 2 of A248461.

Sequence in context: A051959 A117327 A153371 * A169880 A282554 A240151

Adjacent sequences: A248460 A248461 A248462 * A248464 A248465 A248466

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 06 2014

STATUS

approved

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Last modified February 1 05:06 EST 2023. Contains 359981 sequences. (Running on oeis4.)