A163434 Number of different fixed (possibly) disconnected tetrominoes bounded tightly by an n X n square.
0, 1, 70, 425, 1426, 3577, 7526, 14065, 24130, 38801, 59302, 87001, 123410, 170185, 229126, 302177, 391426, 499105, 627590, 779401, 957202, 1163801, 1402150, 1675345, 1986626, 2339377, 2737126, 3183545, 3682450, 4237801, 4853702
Offset: 1
Examples
a(2)=1: the (connected) square tetromino.
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Mathematica
Join[{0}, Table[(2 n^2 - 4 n + 1)*(3 n^2 - 6 n + 1), {n, 2, 50}]] (* or *) Join[{0}, LinearRecurrence[{5,-10,10,-5,1}, {1, 70, 425, 1426, 3577}, 50]] (* G. C. Greubel, Dec 23 2016 *) -
PARI
concat([0], Vec(x^2*(1+65*x+85*x^2-9*x^3+2*x^4)/(1-x)^5 + O(x^50))) \\ G. C. Greubel, Dec 23 2016
Formula
a(n) = (2n^2 -4n +1)*(3n^2 -6n +1), n>1.
G.f.: x^2*(1+65*x+85*x^2-9*x^3+2*x^4)/(1-x)^5. - Colin Barker, Apr 25 2012
E.g.f.: (6*x^4 + 12*x^3 - x^2 + x + 1)*exp(x) - 2 x - 1. - G. C. Greubel, Dec 23 2016