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%I #12 Feb 06 2017 18:27:11
%S 1,1,1,1,1,1,1,10,21,34,49,66,85,106,256,535,985,1654,2596,3871,5545,
%T 9391,16956,30589,53481,89851,145152,226297,364656,610062,1045297,
%U 1799392,3065145,5121255,8359876,13624960,22431292,37434945,63098713,106641142,179356873
%N Number of tilings of a 14 X n rectangle using 2n heptominoes of shape I.
%H Alois P. Heinz, <a href="/A250664/b250664.txt">Table of n, a(n) for n = 0..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Heptomino">Heptomino</a>
%F G.f.: See Maple program.
%p 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
%p -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):
%p a:= n-> coeff(series(gf, x, n+1), x, n):
%p seq(a(n), n=0..50);
%Y Column k=7 of A250662.
%Y Cf. A251076.
%K nonn,easy
%O 0,8
%A _Alois P. Heinz_, Nov 26 2014
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