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A239269 Number of domicule tilings of a 7 X 2n grid. 2
1, 85, 55553, 55263473, 57228320561, 59567383578529, 62052716855623473, 64650946142760951261, 67359700036979921768537, 70182277765258094462607893, 73123194329034252403047192825, 76187359457974079841046201710145, 79379928242473326520049884806574585 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A domicule is either a domino or it is formed by the union of two neighboring unit squares connected via their corners.  In a tiling the connections of two domicules are allowed to cross each other.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

FORMULA

G.f.: see Maple program.

MAPLE

gf:= -(7893703125*x^35 +1178708506875*x^34 -9471431967075*x^33 -25190320844889*x^32 -9539586874311708*x^31 -410493220050893916*x^30 +575920683970775496*x^29 +18726269678802107312*x^28 -29034124354337289144*x^27 -271800359878010634120*x^26 +133177110631012683908*x^25 +3079586993271739345580*x^24 +7730783335738153680196*x^23 -13782583787844763915596*x^22 -24366977853323332846216*x^21 +42038513809989658019568*x^20

-2063678050944576884326*x^19 -12638594920205361440138*x^18 -17386843344014733116586*x^17 +12426575461737923667314*x^16 +1343983627937159538828*x^15 -1998626828626429701652*x^14 +204472622438434512248*x^13 +108140323865267622480*x^12 -35469623048779376672*x^11 +4748719687765155200*x^10 -335752562560949100*x^9 +11627286098346812*x^8 -19234625432244*x^7 -14741830904132*x^6 +600036486728*x^5 -11552831472*x^4 +119161193*x^3 -637033*x^2 +1525*x-1) /

(165767765625*x^36 +24700588841250*x^35 -207544264492950*x^34 -563331132080334*x^33 -200395385497647183*x^32 -8534040529839498708*x^31 +14421739565668843632*x^30 +373620115417467491764*x^29 -641619825956467695364*x^28 -5341798879289372842564*x^27 +3704450681906208094872*x^26 +62112119203321800127524*x^25 +139265952634127843836508*x^24 -281856942688598542445972*x^23 -423329608424574749966944*x^22 +819513105984638655264308*x^21 -131429598068784609902586*x^20 -183950660210880870863984*x^19

-338671775387238895856372*x^18 +266233302665002558298712*x^17 +10903080854445516491318*x^16 -42213214899090813823964*x^15 +6893131124521390078704*x^14 +1965020207232094351100*x^13 -889373505806780285412*x^12 +147961219061817772452*x^11 -13450469929625673736*x^10 +688585418250974364*x^9 -15421722568196676*x^8 -288352000782012*x^7 +30787771291904*x^6 -957729947364*x^5 +15806918761*x^4 -146042386*x^3 +718330*x^2 -1610*x+1):

a:= n-> coeff(series(gf, x, n+1), x, n):

seq(a(n), n=0..20);

CROSSREFS

Even bisection of column k=7 of A239264.

Sequence in context: A015338 A181015 A131750 * A068749 A172826 A196886

Adjacent sequences:  A239266 A239267 A239268 * A239270 A239271 A239272

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Mar 13 2014

STATUS

approved

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Last modified April 20 22:22 EDT 2019. Contains 322310 sequences. (Running on oeis4.)