A226547 Number of squares in all tilings of a 4 X n rectangle using integer-sided square tiles.

0, 4, 25, 98, 386, 1402, 4938, 16936, 57020, 189172, 620397, 2015456, 6496391, 20801576, 66231279, 209847980, 662049349, 2080850248, 6518383898, 20358327362, 63413001935, 197042859318, 610922240964, 1890331512546, 5838350817615, 18001432735438, 55417333344241

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,2,-12,-11,2,10,6,-1,-2,-1).

Formula

G.f.: (x^5+6*x^4-8*x^3-10*x^2+9*x+4)*x/((x+1)^2*(x^4-3*x+1)^2).

a(n) = 4*a(n-1) + 2*a(n-2) - 12*a(n-3) - 11*a(n-4) + 2*a(n-5) + 10*a(n-6) + 6*a(n-7) - a(n-8) - 2*a(n-9) - a(n-10) for n>9. - Colin Barker, Jun 07 2020

Prog

(PARI) concat(0, Vec(x*(4 + 9*x - 10*x^2 - 8*x^3 + 6*x^4 + x^5) / ((1 + x)^2*(1 - 3*x + x^4)^2) + O(x^30))) \\ Colin Barker, Jun 07 2020

Crossrefs

Column k=4 of A226545.

Cf. A054856.

Sequence in context: A323967 A195509 A027949 * A264167 A152215 A231175

Adjacent sequences: A226544 A226545 A226546 * A226548 A226549 A226550

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 10 2013

Status

approved