cp's OEIS Frontend

A237355 The number of tilings of the 3 X 4 X n room by 1 X 1 X 3 boxes.

%I A237355 #19 Mar 01 2024 11:28:03
%S A237355 1,3,9,92,749,4430,30076,217579,1479055,10046609,69575902,479035195,
%T A237355 3284657308,22593041544,155444686265,1068352050847,7344626541715,
%U A237355 50504764148658,347234420131143,2387280989007848,16413850076764282,112852648679477233,775901649656851817
%N A237355 The number of tilings of the 3 X 4 X n room by 1 X 1 X 3 boxes.
%C A237355 The count compiles all arrangements without respect to symmetry: Stacks that are equivalent after rotations or flips through any of the 3 axes or 3 planes are counted with multiplicity.
%C A237355 The rational generating function p(x)/q(x) is qualified in the Maple section for argument x=z^4.
%H A237355 Alois P. Heinz, <a href="/A237355/b237355.txt">Table of n, a(n) for n = 0..1000</a>
%H A237355 R. J. Mathar, <a href="http://arxiv.org/abs/1406.7788">Tilings of rectangular regions by rectangular tiles: counts derived from transfer matrices</a>, arXiv:1406.7788 [math.CO], eq. (41).
%H A237355 <a href="/index/Rec#order_90">Index entries for linear recurrences with constant coefficients</a>, 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).
%p A237355 A237355 := proc(n)
%p A237355 p :=
%p A237355 -(-1 +3396185*z^268 +126*z^12 -1276*z^28 +5*z^8 +
%p A237355 5283231061*z^124-1577588*z^52 -13645425693*z^152 +
%p A237355 144704015*z^244 -455*z^20 +13238456*z^260 +31819046103*z
%p A237355 ^156 -z^320 +25108196325*z^148 -93044*z^44 -2901338989*z
%p A237355 ^128 -10*z^336 -2163597596*z^216 +10067*z^32 -29481842170
%p A237355 *z^168 -27774785437*z^144 +2*z^4 -4*z^340 -18745905736
%p A237355 *z^176 +7299716699*z^140 +21*z^332 -501*z^312 +
%p A237355 32101048863*z^172 -71881307*z^76 +153863*z^36 +13993826*z
%p A237355 ^64 +35536*z^292 +10372*z^300 -21028*z^296 -28*z^324
%p A237355 +21886734767*z^180 +2407716*z^68 +91622*z^40 -23376175*z
%p A237355 ^80 -24005339291*z^184 +100677112*z^92 -7169*z^304 +1184*
%p A237355 z^316 +222741*z^56 -192795426*z^100 +5270172488*z^108 -
%p A237355 57*z^328 +25361870*z^252 -4094967*z^264 +943065389*z^
%p A237355 116 +19724145370*z^132 -32733186254*z^160 +18663190295*z^
%p A237355 164 +561417344*z^84 -1224595901*z^224 +14015301065*z^188 -
%p A237355 2024669*z^272 -11369197887*z^120 +337006779*z^236 -
%p A237355 990719131*z^112 -25766687*z^256 -6333*z^24 +207060338*z^
%p A237355 88 +19722918*z^60 -123289650*z^72 -73800398*z^248 +651316
%p A237355 *z^276 -309189319*z^104 -93*z^16 -14025522915*z^136 -
%p A237355 2171925*z^48 +13808940292*z^196 +671*z^308 +2217864262*z
%p A237355 ^220 -634809849*z^232 +617029016*z^228 +259296*z^284 -
%p A237355 7967920024*z^200 -6205639852*z^208 +3519281640*z^212 +
%p A237355 5961180966*z^204 +z^348 -12884456696*z^192 -1943914891*z^
%p A237355 96 -105001*z^288 -138606683*z^240 -319172*z^280) ;
%p A237355 p := algsubs(z^4=x,p) ;
%p A237355 q :=
%p A237355 1-
%p A237355 60815785*z^268 -176*z^12 -1074*z^28 +z^8 -2139678101*z
%p A237355 ^124 +4517295*z^52 +32366552001*z^152 -1795023861*z^244 +
%p A237355 293*z^20 -196601781*z^260 -132185701967*z^156 +1278*z^
%p A237355 320 -71881449601*z^148 +59839*z^44 -2160878871*z^128 -65*
%p A237355 z^336 +22568613842*z^216 -7860*z^32 +142211822794*z^168 +
%p A237355 104511366128*z^144 -5*z^4 -65*z^340 +91273082294*z^176
%p A237355 -6729477185*z^140 +85*z^332 +12778*z^312 -144862794083*z
%p A237355 ^172 +339177827*z^76 -272389*z^36 -50928278*z^64 -559851*
%p A237355 z^292 -211745*z^300 +506788*z^296 -130*z^324 -
%p A237355 126560496081*z^180 -5385773*z^68 -183389*z^40 +33326860*z
%p A237355 ^80 +132197432121*z^184 -41410295*z^92 +55563*z^304 -
%p A237355 12700*z^316 +105217*z^56 +3679914785*z^100 -17881094620*z
%p A237355 ^108 +1761*z^328 -436930703*z^252 +z^360 +73736037*z^
%p A237355 264 +1839198593*z^116 -70543105470*z^132 +119917584642*z^
%p A237355 160 -67890453774*z^164 -1656296393*z^84 +12491943945*z^224
%p A237355 -86012823396*z^188 +31180618*z^272 -7*z^352 +39629953212*
%p A237355 z^120 -3979624295*z^236 -4934247701*z^112 +375021274*z^
%p A237355 256 +10064*z^24 -1420714989*z^88 -44954256*z^60 +322607030
%p A237355 *z^72 +997380768*z^248 -10961366*z^276 -385369833*z^104
%p A237355 +323*z^16 +27232379880*z^136 +4323330*z^48 -92190746241*
%p A237355 z^196 -36708*z^308 -20609808196*z^220 +6816233581*z^232 -
%p A237355 7780358999*z^228 -4209081*z^284 +59232895357*z^200 +
%p A237355 49378215194*z^208 -30858791790*z^212 -51135748066*z^204 -11
%p A237355 *z^348 +90553404712*z^192 +6265092815*z^96 +1578469*z^
%p A237355 288 +33*z^344 +2091442392*z^240 +7072305*z^280 ;
%p A237355 q := algsubs(z^4=x,q) ;
%p A237355 coeftayl(p/q,x=0,n) ;
%p A237355 end proc:
%p A237355 seq(A237355(n),n=0..20) ;
%Y A237355 Cf. A233247 (2 X 3 X n rooms), A233289 (3 X 3 X n rooms), A273474.
%K A237355 nonn
%O A237355 0,2
%A A237355 _R. J. Mathar_, Feb 07 2014