A352591 Number of tilings of a 5 X n rectangle using 2 X 2 and 1 X 1 tiles and dominoes.

1, 8, 306, 7546, 210690, 5684228, 154869092, 4207660108, 114411435032, 3110251075956, 84557403666284, 2298788023809188, 62495515282157930, 1699018055917569318, 46189937030173640586, 1255731173553810109440, 34138623221740999081824, 928101175618008434398704

Offset

0,2

Comments

The sequence is based on A352589.

Links

Table of n, a(n) for n=0..17.

Index entries for linear recurrences with constant coefficients, signature (15, 361, -200, -17183, 6963, 320541, -363476, -2096695, 2659007, 6914929, -7710612, -13172634, 10195340, 14247416, -5770992, -7493472, 1420800, 1734912, -133632, -138240).

Formula

G.f.: (1 - 7*x - 175*x^2 + 268*x^3 + 5817*x^4 - 8527*x^5 - 62465*x^6 + 86808*x^7 + 299229*x^8 - 339035*x^9 - 761445*x^10 + 575980*x^11 + 1035378*x^12 - 409804*x^13 - 662520*x^14 + 131472*x^15 + 184320*x^16 - 16704*x^17 - 17280*x^18) / (1 - 15*x - 361*x^2 + 200*x^3 + 17183*x^4 - 6963*x^5 - 320541*x^6 + 363476*x^7 + 2096695*x^8 - 2659007*x^9 - 6914929*x^10 + 7710612*x^11 + 13172634*x^12 - 10195340*x^13 - 14247416*x^14 + 5770992*x^15 + 7493472*x^16 - 1420800*x^17 - 1734912*x^18 + 133632*x^19 + 138240*x^20).

Recurrence: a(n) = 15*a(n-1) + 361*a(n-2) - 200*a(n-3) - 17183*a(n-4) + 6963*a(n-5) + 320541*a(n-6) - 363476*a(n-7) - 2096695*a(n-8) + 2659007*a(n-9) + 6914929*a(n-10) - 7710612*a(n-11) - 13172634*a(n-12) + 10195340*a(n-13) + 14247416*a(n-14) - 5770992*a(n-15) - 7493472*a(n-16) + 1420800*a(n-17) + 1734912*a(n-18) - 133632*a(n-19) - 138240*a(n-20).

Crossrefs

Cf. A352589, A352590.

Sequence in context: A316647 A316175 A317457 * A220998 A222091 A193812

Adjacent sequences: A352588 A352589 A352590 * A352592 A352593 A352594

Keyword

nonn,easy

Author

Gerhard Kirchner, Mar 22 2022

Status

approved