A237355 The number of tilings of the 3 X 4 X n room by 1 X 1 X 3 boxes.
1, 3, 9, 92, 749, 4430, 30076, 217579, 1479055, 10046609, 69575902, 479035195, 3284657308, 22593041544, 155444686265, 1068352050847, 7344626541715, 50504764148658, 347234420131143, 2387280989007848, 16413850076764282, 112852648679477233, 775901649656851817
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- R. J. Mathar, Tilings of rectangular regions by rectangular tiles: counts derived from transfer matrices, arXiv:1406.7788 [math.CO], eq. (41).
- Index entries for linear recurrences with constant coefficients, signature (5, -1, 176, -323, -293, -10064, 1074, 7860, 272389, 183389, -59839, -4323330, -4517295, -105217, 44954256, 50928278, 5385773, -322607030, -339177827, -33326860, 1656296393, 1420714989, 41410295, -6265092815, -3679914785, 385369833, 17881094620, 4934247701, -1839198593, -39629953212, 2139678101, 2160878871, 70543105470, -27232379880, 6729477185, -104511366128, 71881449601, -32366552001, 132185701967, -119917584642, 67890453774, -142211822794, 144862794083, -91273082294, 126560496081, -132197432121, 86012823396, -90553404712, 92190746241, -59232895357, 51135748066, -49378215194, 30858791790, -22568613842, 20609808196, -12491943945, 7780358999, -6816233581, 3979624295, -2091442392, 1795023861, -997380768, 436930703, -375021274, 196601781, -73736037, 60815785, -31180618, 10961366, -7072305, 4209081, -1578469, 559851, -506788, 211745, -55563, 36708, -12778, 12700, -1278, 130, -1761, -85, 65, 65, -33, 11, 7, 0, -1).
Programs
-
Maple
A237355 := proc(n) p := -(-1 +3396185*z^268 +126*z^12 -1276*z^28 +5*z^8 + 5283231061*z^124-1577588*z^52 -13645425693*z^152 + 144704015*z^244 -455*z^20 +13238456*z^260 +31819046103*z ^156 -z^320 +25108196325*z^148 -93044*z^44 -2901338989*z ^128 -10*z^336 -2163597596*z^216 +10067*z^32 -29481842170 *z^168 -27774785437*z^144 +2*z^4 -4*z^340 -18745905736 *z^176 +7299716699*z^140 +21*z^332 -501*z^312 + 32101048863*z^172 -71881307*z^76 +153863*z^36 +13993826*z ^64 +35536*z^292 +10372*z^300 -21028*z^296 -28*z^324 +21886734767*z^180 +2407716*z^68 +91622*z^40 -23376175*z ^80 -24005339291*z^184 +100677112*z^92 -7169*z^304 +1184* z^316 +222741*z^56 -192795426*z^100 +5270172488*z^108 - 57*z^328 +25361870*z^252 -4094967*z^264 +943065389*z^ 116 +19724145370*z^132 -32733186254*z^160 +18663190295*z^ 164 +561417344*z^84 -1224595901*z^224 +14015301065*z^188 - 2024669*z^272 -11369197887*z^120 +337006779*z^236 - 990719131*z^112 -25766687*z^256 -6333*z^24 +207060338*z^ 88 +19722918*z^60 -123289650*z^72 -73800398*z^248 +651316 *z^276 -309189319*z^104 -93*z^16 -14025522915*z^136 - 2171925*z^48 +13808940292*z^196 +671*z^308 +2217864262*z ^220 -634809849*z^232 +617029016*z^228 +259296*z^284 - 7967920024*z^200 -6205639852*z^208 +3519281640*z^212 + 5961180966*z^204 +z^348 -12884456696*z^192 -1943914891*z^ 96 -105001*z^288 -138606683*z^240 -319172*z^280) ; p := algsubs(z^4=x,p) ; q := 1- 60815785*z^268 -176*z^12 -1074*z^28 +z^8 -2139678101*z ^124 +4517295*z^52 +32366552001*z^152 -1795023861*z^244 + 293*z^20 -196601781*z^260 -132185701967*z^156 +1278*z^ 320 -71881449601*z^148 +59839*z^44 -2160878871*z^128 -65* z^336 +22568613842*z^216 -7860*z^32 +142211822794*z^168 + 104511366128*z^144 -5*z^4 -65*z^340 +91273082294*z^176 -6729477185*z^140 +85*z^332 +12778*z^312 -144862794083*z ^172 +339177827*z^76 -272389*z^36 -50928278*z^64 -559851* z^292 -211745*z^300 +506788*z^296 -130*z^324 - 126560496081*z^180 -5385773*z^68 -183389*z^40 +33326860*z ^80 +132197432121*z^184 -41410295*z^92 +55563*z^304 - 12700*z^316 +105217*z^56 +3679914785*z^100 -17881094620*z ^108 +1761*z^328 -436930703*z^252 +z^360 +73736037*z^ 264 +1839198593*z^116 -70543105470*z^132 +119917584642*z^ 160 -67890453774*z^164 -1656296393*z^84 +12491943945*z^224 -86012823396*z^188 +31180618*z^272 -7*z^352 +39629953212* z^120 -3979624295*z^236 -4934247701*z^112 +375021274*z^ 256 +10064*z^24 -1420714989*z^88 -44954256*z^60 +322607030 *z^72 +997380768*z^248 -10961366*z^276 -385369833*z^104 +323*z^16 +27232379880*z^136 +4323330*z^48 -92190746241* z^196 -36708*z^308 -20609808196*z^220 +6816233581*z^232 - 7780358999*z^228 -4209081*z^284 +59232895357*z^200 + 49378215194*z^208 -30858791790*z^212 -51135748066*z^204 -11 *z^348 +90553404712*z^192 +6265092815*z^96 +1578469*z^ 288 +33*z^344 +2091442392*z^240 +7072305*z^280 ; q := algsubs(z^4=x,q) ; coeftayl(p/q,x=0,n) ; end proc: seq(A237355(n),n=0..20) ;
Comments