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A049222 Number of horizontally convex n-ominoes in which the top row has exactly 1 square, which is not above the rightmost square in the second row and the rightmost square in the second row is above the leftmost square in the third row. 2
0, 0, 0, 1, 4, 13, 41, 130, 415, 1329, 4260, 13657, 43781, 140346, 449891, 1442157, 4622932, 14819125, 47503729, 152276498, 488132887, 1564743865, 5015895108, 16078800033, 51541709869, 165220529546, 529625878779, 1697752526549 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..28.

Dean Hickerson, Counting Horizontally Convex Polyominoes, J. Integer Sequences, Vol. 2 (1999), #99.1.8.

Index entries for linear recurrences with constant coefficients, signature (5, -7, 4).

FORMULA

G.f.: x^4 (1-x)/(1-5x+7x^2-4x^3).

a(n) = 5*a(n-1) - 7*a(n-2) + 4*a(n-3) for n >= 6.

a(n) = a(n-1) + A049220(n-1) for n >= 2.

MATHEMATICA

a[ n_ ] := a[ n ]=If[ n<6, {0, 0, 0, 1, 4}[ [ n ] ], 5a[ n-1 ]-7a[ n-2 ]+4a[ n-3 ] ]

Join[{0, 0, 0}, LinearRecurrence[{5, -7, 4}, {0, 1, 4}, 30]] (* or *) CoefficientList[ Series[x^4 (1-x)/(1-5x+7x^2-4x^3), {x, 0, 30}], x] (* Harvey P. Dale, May 10 2011 *)

CROSSREFS

Cf. A049220.

Sequence in context: A268989 A190214 A052529 * A239249 A141364 A001453

Adjacent sequences:  A049219 A049220 A049221 * A049223 A049224 A049225

KEYWORD

nonn,easy

AUTHOR

Dean Hickerson, Aug 10 1999

STATUS

approved

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Last modified February 17 16:26 EST 2018. Contains 299296 sequences. (Running on oeis4.)