A220057 - OEIS

%I #7 Aug 20 2024 09:29:56

%S 1,1,655,17511,1328849,65564239,3814023955,207866584389,

%T 11621270470141,643234164533111,35743258143250665,1983110281248178907,

%U 110094091718725808219,6110504997318928433203,339180718810796793005395,18826477870730711026769043

%N Number of tilings of a 7 X n rectangle using right trominoes and 1 X 1 tiles.

%H Alois P. Heinz, <a href="/A220057/b220057.txt">Table of n, a(n) for n = 0..300</a>

%H <a href="/index/Rec#order_55">Index entries for linear recurrences with constant coefficients</a>, signature (31, 1688, -11130, -459918, 3166506, 40112677, -345723568, -1333668560, 18915874110, -20132638419, -340706701381, 1131454106758, 1800169591293, -14547686180172, 10887029502746, 77700424321275, -170596686592062, -132867339076434, 814120637502953, -408118945300204, -1874303491278113, 2371447568852003, 2065885358158550, -4510347925558337, -1768155209701568, 5626569971126797, 3093435933277591, -8190510139279992, -2502197734475072, 9273148424569143, -314261646620241, -5569775487698427, 516945589065495, 1847002437609681, 588598730671956, -502432621307848, -485326816160748, 41192473052820, 191502873476778, 53306213357242, -44398553938820, -28149773265720, 14071419586760, 5403011349240, -6450496694256, -6085229826624, -1539089548288, -55320676736, 84819354752, 9551531264, 6799316992, 3599682560, 134983680, -12386304, 1048576).

%F G.f.: see Maple program.

%p gf:= (196608*x^53 +15716352*x^52 +82890752*x^51 -81387520*x^50 +2420729856*x^49 -5502464896*x^48 +11135136384*x^47 -2587529280*x^46 -242120057280*x^45 -391566462048*x^44 -677756970360*x^43 -26891699024*x^42 +3419049690968*x^41 -898216784632*x^40 -8630220265938*x^39 +11892744055744*x^38 +12674156157904*x^37

%p -23326232274170*x^36 -8460520836030*x^35 -49526668612724*x^34 -52615082821909*x^33 +385796302646490*x^32 -89063359404187*x^31 -689833337938642*x^30 +276301559560831*x^29 +939553216589439*x^28 -751421966953043*x^27 -387235565854614*x^26 +367601964623911*x^25 +391200153596741*x^24 -321438046442330*x^23 -254149045627282*x^22

%p +327959797230961*x^21 -30793906263310*x^20 -105485377717340*x^19 +46988439121753*x^18 +10650397716161*x^17 -12878278811627*x^16 +1803973124746*x^15 +1212527797540*x^14 -447484692550*x^13 +13047687869*x^12 +14482637535*x^11 -3330884126*x^10 +1108885391*x^9 -182374621*x^8 -34669281*x^7 +8700029*x^6 +605086*x^5 -151416*x^4 -6648*x^3 +1064*x^2 +30*x -1) /

%p (1048576*x^55 -12386304*x^54 +134983680*x^53 +3599682560*x^52 +6799316992*x^51 +9551531264*x^50 +84819354752*x^49 -55320676736*x^48 -1539089548288*x^47 -6085229826624*x^46 -6450496694256*x^45 +5403011349240*x^44 +14071419586760*x^43 -28149773265720*x^42 -44398553938820*x^41 +53306213357242*x^40 +191502873476778*x^39

%p +41192473052820*x^38 -485326816160748*x^37 -502432621307848*x^36 +588598730671956*x^35 +1847002437609681*x^34 +516945589065495*x^33 -5569775487698427*x^32 -314261646620241*x^31 +9273148424569143*x^30 -2502197734475072*x^29 -8190510139279992*x^28 +3093435933277591*x^27 +5626569971126797*x^26 -1768155209701568*x^25 -4510347925558337*x^24 +2065885358158550*x^23 +2371447568852003*x^22 -1874303491278113*x^21

%p -408118945300204*x^20 +814120637502953*x^19 -132867339076434*x^18 -170596686592062*x^17 +77700424321275*x^16 +10887029502746*x^15 -14547686180172*x^14 +1800169591293*x^13 +1131454106758*x^12 -340706701381*x^11 -20132638419*x^10 +18915874110*x^9 -1333668560*x^8 -345723568*x^7 +40112677*x^6 +3166506*x^5 -459918*x^4 -11130*x^3 +1688*x^2 +31*x -1):

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

%p seq(a(n), n=0..30);

%Y Column k=7 of A220054.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Dec 03 2012