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

0,8

Links

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

Wikipedia, Heptomino

Formula

G.f.: See Maple program.

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);

Crossrefs

Column k=7 of A250662.

Cf. A251076.

Sequence in context: A072806 A189402 A051942 * A082581 A075846 A164714

Adjacent sequences: A250661 A250662 A250663 * A250665 A250666 A250667

Keyword

nonn,easy

Author

Alois P. Heinz, Nov 26 2014

Status

approved