STATUS
editing
approved
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Revision History for A289792
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LINKS
<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
STATUS
approved
editing
STATUS
proposed
approved
STATUS
editing
proposed
NAME
allocated for Eric W. Weisstein
Number of 4-cycles in the n-tetrahedral graph.
DATA
0, 0, 0, 0, 90, 540, 1995, 5775, 14280, 31500, 63630, 119790, 212850, 360360, 585585, 918645, 1397760, 2070600, 2995740, 4244220, 5901210, 8067780, 10862775, 14424795, 18914280, 24515700, 31439850, 39926250, 50245650, 62702640, 77638365, 95433345, 116510400
OFFSET
1,5
COMMENTS
Extended to a(1)-a(5) using the formula.
LINKS
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TetrahedralGraph.html">Tetrahedral Graph</a>
FORMULA
a(n) = binomial(n - 1, 4) * (210 - 41*n + 7*n^2)/2.
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7).
G.f.: (-15*x^5*(6 - 6*x + 7*x^2))/(-1 + x)^7.
MATHEMATICA
Table[Binomial[n - 1, 4] (210 - 41 n + 7 n^2)/2, {n, 20}]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 0, 90, 540, 1995}, 20]
CoefficientList[Series[-((15 x^4 (6 - 6 x + 7 x^2))/(-1 + x)^7), {x, 0, 20}], x]
KEYWORD
allocated
nonn,easy
AUTHOR
Eric W. Weisstein, Jul 12 2017
STATUS
approved
editing
NAME
allocated for Eric W. Weisstein
KEYWORD
allocated
STATUS
approved