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, 32, 320, 1784, 7040, 22104, 58980, 139320, 299343, 596200, 1115972, 1983488, 3374150, 5527952, 8765880, 13508880, 20299581, 29826960, 42954136, 60749480, 84521228, 115855784, 156659900, 209206920, 276187275, 360763416, 466629372, 598075120, 760055954, 958267040, 1199223344, 1490345120
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]
- Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
Programs
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Mathematica
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,32,320,1784,7040,22104,58980,139320},40] (* Harvey P. Dale, Aug 17 2019 *) -
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
Formula
G.f.: (1 + 24*x + 92*x^2 + 64*x^3 + 6*x^4) / (1 - x)^8.
From Colin Barker, Jan 11 2017: (Start)
a(n) = (5040 + 22164*n + 43092*n^2 + 46963*n^3 + 30240*n^4 + 11326*n^5 + 2268*n^6 + 187*n^7) / 5040.
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.
(End)