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A049222
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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.
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2
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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; internal format)
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OFFSET
| 1,5
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REFERENCES
| Dean Hickerson, Counting Horizontally Convex Polyominoes, J. Integer Sequences, Vol. 2 (1999), #99.1.8.
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LINKS
| Hickerson reference.
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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
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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] (* From Harvey P. Dale, May 10 2011 *)
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CROSSREFS
| a(n) = a(n-1) + A049220(n-1) for n >= 2
Sequence in context: A070428 A190214 A052529 * A001453 A141364 A005002
Adjacent sequences: A049219 A049220 A049221 * A049223 A049224 A049225
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KEYWORD
| nonn,easy
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AUTHOR
| Dean Hickerson (dean.hickerson(AT)yahoo.com), Aug 10 1999
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