A366324 Number of tilings of a 5 X n rectangle using n pentominoes of shapes T, W, Y, X.

1, 0, 0, 0, 2, 2, 8, 0, 22, 40, 134, 100, 266, 448, 1610, 2454, 4806, 7064, 19774, 38320, 81174, 128604, 277540, 553762, 1222204, 2210510, 4352240, 8339138, 17869740, 34938578, 69204722, 131277114, 267512514, 533554754, 1074570418, 2076822340, 4120024394

Offset: 0

Author

Alois P. Heinz, Nov 14 2023

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3367
• Wikipedia, Pentomino
• Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 5, 9, 6, -5, 5, 8, 48, -13, -37, -36, 58, 37, -37, -94, 8, 56, 188, -254, -181, 92, -55, 155, -267, -346, 91, 444, -61, 56, -258, 36, 371, 116, -122, -94, 40, 116, 64, 0, 16, 0, 32).

Crossrefs

Cf. A174249, A361250, A372221.

Formula

G.f.: (16*x^42 +32*x^41 +16*x^40 +20*x^39 +8*x^38 +4*x^37 -40*x^36 +8*x^35 +13*x^34 -42*x^33 -84*x^32 +4*x^31 -79*x^30 +82*x^29 +61*x^28 -50*x^27 -33*x^26 +47*x^25 +21*x^24 +36*x^23 -23*x^22 -102*x^21 +16*x^20 +26*x^19 +12*x^18 -14*x^17 -5*x^16 +x^15 +28*x^14 -11*x^12 +x^11 +6*x^10 -4*x^9 +x^8 -3*x^7 +7*x^5 +3*x^4 +x^2 -1) / (32*x^44 +16*x^42 +64*x^40 +116*x^39 +40*x^38 -94*x^37 -122*x^36 +116*x^35 +371*x^34 +36*x^33 -258*x^32 +56*x^31 -61*x^30 +444*x^29 +91*x^28 -346*x^27 -267*x^26 +155*x^25 -55*x^24 +92*x^23 -181*x^22 -254*x^21 +188*x^20 +56*x^19 +8*x^18 -94*x^17 -37*x^16 +37*x^15 +58*x^14 -36*x^13 -37*x^12 -13*x^11 +48*x^10 +8*x^9 +5*x^8 -5*x^7 +6*x^6 +9*x^5 +5*x^4 +x^2 -1).