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#14 by Alois P. Heinz at Thu Jan 16 16:26:07 EST 2020
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#13 by Andrew Howroyd at Thu Jan 16 16:09:15 EST 2020
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#12 by Andrew Howroyd at Thu Jan 16 15:02:07 EST 2020
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| LINKS
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Andrew Howroyd, <a href="/A254152/b254152.txt">Table of n, a(n) for n = 0..200</a>
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Discussion
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| Thu Jan 16
| 16:09
| Andrew Howroyd: The two incorrect terms are those that are >= 10^17, suggesting double precision floating point was used.
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#11 by Andrew Howroyd at Thu Jan 16 14:38:58 EST 2020
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#10 by Andrew Howroyd at Thu Jan 16 14:37:18 EST 2020
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| NAME
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Number of independent sets in the generalized Aztec diamond E(L_9,L_{2m2n-1}).
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| COMMENTS
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E(L_9,L_{2m2n-1}) is the graph with vertices {(a,b) : 1<=a<=9, 1<=b<=2n-1, a+b even} and edges between (a,b) and (c,d) if and only if |a-b|=|c-d|=1.
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Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>
<a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (74,-1450,10672,-34214,50814,-34671,9772,-936).
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| FORMULA
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G.f.: (1 - 42*x + 433*x^2 - 1745*x^3 + 3002*x^4 - 2275*x^5 + 700*x^6 - 72*x^7)/(1 - 74*x + 1450*x^2 - 10672*x^3 + 34214*x^4 - 50814*x^5 + 34671*x^6 - 9772*x^7 + 936*x^8). - Andrew Howroyd, Jan 16 2020
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| PROG
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(PARI) Vec((1 - 42*x + 433*x^2 - 1745*x^3 + 3002*x^4 - 2275*x^5 + 700*x^6 - 72*x^7)/(1 - 74*x + 1450*x^2 - 10672*x^3 + 34214*x^4 - 50814*x^5 + 34671*x^6 - 9772*x^7 + 936*x^8) + O(x^20)) \\ Andrew Howroyd, Jan 16 2020
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#9 by Andrew Howroyd at Wed Jan 15 23:50:00 EST 2020
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| DATA
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1, 32, 1351, 62501, 2976416, 142999897, 6888568813, 332097693792, 16014193762579, 772279980131297, 37243762479698928, 1796118644459454733, 86619824190256627593, 4177339899819872607008, 201457018240598757372431, 372437624796989209715496740529686006497709, 1796118644459454976468541027322402116068858304
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| EXTENSIONS
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a(10)-a(11) corrected and a(12) and beyond from Andrew Howroyd, Jan 15 2020
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| STATUS
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approved
editing
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#8 by N. J. A. Sloane at Tue Jan 27 00:57:48 EST 2015
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#7 by Tom Edgar at Mon Jan 26 11:58:46 EST 2015
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#6 by Tom Edgar at Mon Jan 26 11:58:43 EST 2015
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Number of independent sets in generalized Aztec diamond E(L_9,L_{2m-1})}).
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| STATUS
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proposed
editing
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#5 by Michel Marcus at Mon Jan 26 11:58:26 EST 2015
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