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 A244867 Let G denote the 9-node, 16-edge graph formed from an octagon with main diagonals drawn and a node at the center; a(n) = number of magic labelings of G with magic sum 2n. 1

%I #12 Aug 17 2019 09:30:09

%S 1,32,320,1784,7040,22104,58980,139320,299343,596200,1115972,1983488,

%T 3374150,5527952,8765880,13508880,20299581,29826960,42954136,60749480,

%U 84521228,115855784,156659900,209206920,276187275,360763416,466629372,598075120,760055954,958267040,1199223344,1490345120

%N Let G denote the 9-node, 16-edge graph formed from an octagon with main diagonals drawn and a node at the center; a(n) = number of magic labelings of G with magic sum 2n.

%H Colin Barker, <a href="/A244867/b244867.txt">Table of n, a(n) for n = 0..1000</a>

%H R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F G.f.: (1 + 24*x + 92*x^2 + 64*x^3 + 6*x^4) / (1 - x)^8.

%F From _Colin Barker_, Jan 11 2017: (Start)

%F a(n) = (5040 + 22164*n + 43092*n^2 + 46963*n^3 + 30240*n^4 + 11326*n^5 + 2268*n^6 + 187*n^7) / 5040.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7.

%F (End)

%t LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,32,320,1784,7040,22104,58980,139320},40] (* _Harvey P. Dale_, Aug 17 2019 *)

%o (PARI) Vec((1 + 24*x + 92*x^2 + 64*x^3 + 6*x^4) / (1 - x)^8 + O(x^40)) \\ _Colin Barker_, Jan 11 2017

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jul 07 2014

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Last modified August 6 15:42 EDT 2024. Contains 374974 sequences. (Running on oeis4.)