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A194772 Number of lower triangles of an (n+2) X (n+2) 0..2 array with new values introduced in row major order 0..2 and no element unequal to more than one horizontal or vertical neighbor. 1
7, 17, 41, 95, 219, 493, 1101, 2427, 5311, 11529, 24881, 53399, 114083, 242725, 514581, 1087411, 2291335, 4815681, 10097401, 21126863, 44117867, 91963997, 191384541, 397682155, 825190479, 1710033273, 3539371201, 7317351687 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A194778.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..34

FORMULA

Empirical: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +4*a(n-5).

Conjectures from Colin Barker, May 05 2018: (Start)

G.f.: x*(7 - 4*x - 17*x^2 + 4*x^3 + 12*x^4) / ((1 - x)*(1 + x)^2*(1 - 2*x)^2).

a(n) = (-3*n + 2^(n+3)*(3*n+8) + 17) / 27 for n even.

a(n) = (3*n + 2^(n+3)*(3*n+8) + 10) / 27 for n odd.

(End)

EXAMPLE

All solutions for 3 X 3 including a 2.

..0

..1.1

..1.1.2

CROSSREFS

Cf. A194778.

Sequence in context: A322597 A193214 A184862 * A193546 A268255 A124965

Adjacent sequences:  A194769 A194770 A194771 * A194773 A194774 A194775

KEYWORD

nonn

AUTHOR

R. H. Hardin, Sep 02 2011

STATUS

approved

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Last modified June 20 17:30 EDT 2021. Contains 345189 sequences. (Running on oeis4.)