A293263 Number of fixed polyominoes without holes that have a width of n and height of 3.

1, 15, 106, 582, 2952, 14488, 69982, 335356, 1600624, 7624266, 36279784, 172546968, 820420150, 3900386212, 18541702744, 88140749906, 418982915000, 1991645550032, 9467293435654, 45002706816100, 213919774521224, 1016864234903874, 4833646472767104

Offset: 1

Author

Andrew Howroyd, Oct 04 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (10,-34,49,-29,2,10,-5,-2).

Crossrefs

Row 3 of A232103.

Programs

Mathematica

LinearRecurrence[{10,-34,49,-29,2,10,-5,-2},{1,15,106,582,2952,14488,69982,335356,1600624},30] (* Harvey P. Dale, Jan 22 2024 *)

PARI

Vec((1 + 5*x - 10*x^2 - 17*x^3 + 30*x^4 - 5*x^5 - 14*x^6 + x^7 + x^8)/((1 - x)*(1 - 2*x - x^2)*(1 - 7*x + 12*x^2 - 7*x^3 + 3*x^4 + 2*x^5)) + O(x^40));

Formula

a(n) = 10*a(n-1) - 34*a(n-2) + 49*a(n-3) - 29*a(n-4) + 2*a(n-5) + 10*a(n-6) - 5*a(n-7) - 2*a(n-8) for n > 9.

G.f.: x*(1 + 5*x - 10*x^2 - 17*x^3 + 30*x^4 - 5*x^5 - 14*x^6 + x^7 + x^8)/((1 - x)*(1 - 2*x - x^2)*(1 - 7*x + 12*x^2 - 7*x^3 + 3*x^4 + 2*x^5)).