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Colin Barker, <a href="/A289163/b289163.txt">Table of n, a(n) for n = 1..1000</a>
G.f.: 2*x^34*(5 + 32*x + 57*x^2 + 146*x^3 + 19*x^4 + 104*x^5 + 15*x^6 + 6*x^7) / ((1 - x)^7*(1 + x)^5). - Colin Barker, Jun 27 2017
(PARI) concat(vector(3), Vec(2*x^34*(5 + 32*x + 57*x^2 + 146*x^3 + 19*x^4 + 104*x^5 + 15*x^6 + 6*x^7) / ((1 - x)^7*(1 + x)^5) + O(x^40))) \\ Colin Barker, Jun 27 2017
approved
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<a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,-10,-5,20,0,-20,5,10,-4,-2,1).
a(n) = 2*a(n-1)+4*a(n-2)-10*a(n-3)-5*a(n-4)+20*a(n-5)-20*a(n-7)+5*a(n-8)+10*a(n-9)-4*a(n-10)-2*a(n-11)++a(n-12).
G.f.: 2*x^3*(5 + 32*x + 57*x^2 + 146*x^3 + 19*x^4 + 104*x^5 + 15*x^6 + 6*x^7) / ((1 - x)^7*(1 + x)^5). - Colin Barker, Jun 27 2017
(PARI) concat(vector(3), Vec(2*x^3*(5 + 32*x + 57*x^2 + 146*x^3 + 19*x^4 + 104*x^5 + 15*x^6 + 6*x^7) / ((1 - x)^7*(1 + x)^5) + O(x^40))) \\ Colin Barker, Jun 27 2017
nonn,changed,easy
proposed
editing
editing
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allocated for Eric W. Weisstein
Number of 5-cycles in the n X n black bishop graph.
0, 0, 0, 10, 84, 322, 1172, 2780, 7016, 13532, 27720, 47318, 84796, 133294, 217756, 322392, 492240, 696216, 1009680, 1377474, 1918500, 2541946, 3426852, 4431988, 5816888, 7371572, 9460568, 11782862, 14837004, 18204326, 22551340, 27310384, 33355168, 39932592, 48168480
1,4
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BlackBishopGraph.html">Black Bishop Graph</a>
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
a(n) = (-165 - 282*n + 972*n^2 - 730*n^3 + 280*n^4 - 68*n^5 + 8*n^6 - 5*(-1)^n*(-33 - 26*n + 96*n^2 - 46*n^3 + 6*n^4))/240.
a(n) = 2*a(n-1)+4*a(n-2)-10*a(n-3)-5*a(n-4)+20*a(n-5)-20*a(n-7)+5*a(n-8)+10*a(n-9)-4*a(n-10)-2*a(n-11)++a(n-12).
Table[(-165 - 282 n + 972 n^2 - 730 n^3 + 280 n^4 - 68 n^5 + 8 n^6 - 5 (-1)^n (-33 - 26 n + 96 n^2 - 46 n^3 + 6 n^4))/240, {n, 20}]
LinearRecurrence[{2, 4, -10, -5, 20, 0, -20, 5, 10, -4, -2, 1}, {0, 0, 0, 10, 84, 322, 1172, 2780, 7016, 13532, 27720, 47318}, 20]
allocated
nonn
Eric W. Weisstein, Jun 26 2017
approved
editing