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A248436 Number of length 3+2 0..n arrays with every three consecutive terms having the sum of some two elements equal to twice the third. 1
2, 9, 24, 69, 118, 185, 252, 357, 470, 593, 716, 881, 1046, 1217, 1400, 1621, 1842, 2081, 2320, 2593, 2874, 3161, 3448, 3785, 4126, 4473, 4828, 5213, 5598, 6005, 6412, 6857, 7310, 7769, 8232, 8737, 9242, 9753, 10272, 10833, 11394, 11973, 12552, 13161, 13782 (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) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + 2*a(n-5) - a(n-6) + a(n-7) - a(n-11) + a(n-12) - 2*a(n-13) + a(n-14) - a(n-15) + a(n-16) - a(n-17) + a(n-18).

Also a quadratic polynomial plus a constant quasipolynomial with period 840, the first 12 being:

Empirical for n mod 840 = 0: a(n) = (106/15)*n^2 - (178/15)*n + 1

Empirical for n mod 840 = 1: a(n) = (106/15)*n^2 - (178/15)*n + (34/5)

Empirical for n mod 840 = 2: a(n) = (106/15)*n^2 - (178/15)*n + (67/15)

Empirical for n mod 840 = 3: a(n) = (106/15)*n^2 - (178/15)*n - 4

Empirical for n mod 840 = 4: a(n) = (106/15)*n^2 - (178/15)*n + (17/5)

Empirical for n mod 840 = 5: a(n) = (106/15)*n^2 - (178/15)*n + (2/3)

Empirical for n mod 840 = 6: a(n) = (106/15)*n^2 - (178/15)*n + (9/5)

Empirical for n mod 840 = 7: a(n) = (106/15)*n^2 - (178/15)*n - (56/5)

Empirical for n mod 840 = 8: a(n) = (106/15)*n^2 - (178/15)*n - (1/3)

Empirical for n mod 840 = 9: a(n) = (106/15)*n^2 - (178/15)*n + (22/5)

Empirical for n mod 840 = 10: a(n) = (106/15)*n^2 - (178/15)*n + 5

Empirical for n mod 840 = 11: a(n) = (106/15)*n^2 - (178/15)*n - (128/15).

Empirical g.f.: x*(2 + 7*x + 17*x^2 + 52*x^3 + 66*x^4 + 117*x^5 + 124*x^6 + 200*x^7 + 175*x^8 + 222*x^9 + 167*x^10 + 210*x^11 + 118*x^12 + 113*x^13 + 52*x^14 + 54*x^15 - x^16 + x^17) / ((1 - x)^3*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 + x^4)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Nov 08 2018

EXAMPLE

Some solutions for n=6:

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

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

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

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

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

CROSSREFS

Row 3 of A248433.

Sequence in context: A274543 A079997 A275260 * A222667 A122006 A200086

Adjacent sequences:  A248433 A248434 A248435 * A248437 A248438 A248439

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 06 2014

STATUS

approved

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Last modified April 15 01:24 EDT 2021. Contains 342974 sequences. (Running on oeis4.)