A250664 Number of tilings of a 14 X n rectangle using 2n heptominoes of shape I.

1, 1, 1, 1, 1, 1, 1, 10, 21, 34, 49, 66, 85, 106, 256, 535, 985, 1654, 2596, 3871, 5545, 9391, 16956, 30589, 53481, 89851, 145152, 226297, 364656, 610062, 1045297, 1799392, 3065145, 5121255, 8359876, 13624960, 22431292, 37434945, 63098713, 106641142, 179356873

Offset: 0

Author

Alois P. Heinz, Nov 26 2014

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Wikipedia, Heptomino

Crossrefs

Column k=7 of A250662.

Cf. A251076.

Programs

Maple

gf:= -(x^21 +x^18 -2*x^15 -3*x^14 -2*x^12 -2*x^11 +x^9 +2*x^8 +3*x^7 +x^6 +x^5 +x^4-1) *(x-1)^6 *(x^6+x^5+x^4+x^3+x^2+x+1)^6 / (x^70 +x^67 -3*x^64 -10*x^63 -3*x^61 -9*x^60 +3*x^58 +23*x^57 +45*x^56 +3*x^55 +21*x^54 +36*x^53 -x^52 -19*x^51 -76*x^50 -121*x^49 -18*x^48 -63*x^47 -84*x^46 +6*x^45 +51*x^44 +140*x^43 +216*x^42 +45*x^41 +105*x^40 +126*x^39
-15*x^38 -75*x^37 -154*x^36 -267*x^35 -60*x^34 -105*x^33 -126*x^32 +20*x^31 +65*x^30 +98*x^29 +236*x^28 +45*x^27 +63*x^26 +90*x^25 -15*x^24 -33*x^23 -40*x^22 -153*x^21 -18*x^20 -33*x^19 -48*x^18 +6*x^17 +15*x^16 +8*x^15 +69*x^14 +9*x^13 +9*x^12 +15*x^11 -x^10 -x^9 +5*x^8 -17*x^7 -x^4 -x +1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..50);

Formula

G.f.: See Maple program.