|
%I #11 Aug 29 2015 02:15:35
%S 1,85,55553,55263473,57228320561,59567383578529,62052716855623473,
%T 64650946142760951261,67359700036979921768537,
%U 70182277765258094462607893,73123194329034252403047192825,76187359457974079841046201710145,79379928242473326520049884806574585
%N Number of domicule tilings of a 7 X 2n grid.
%C 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.
%H Alois P. Heinz, <a href="/A239269/b239269.txt">Table of n, a(n) for n = 0..300</a>
%F G.f.: see Maple program.
%p 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
%p -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) /
%p (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
%p -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):
%p a:= n-> coeff(series(gf, x, n+1), x, n):
%p seq(a(n), n=0..20);
%Y Even bisection of column k=7 of A239264.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Mar 13 2014
| 