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.

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

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