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

Author

Dean Hickerson, Aug 10 1999

Keywords

• nonn
• easy

Links

• 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).

Crossrefs

Cf. A049220.

Programs

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 *)

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.