

A244867


Let G denote the 9node, 16edge 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



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
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OFFSET

0,2


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R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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).


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(n1)  28*a(n2) + 56*a(n3)  70*a(n4) + 56*a(n5)  28*a(n6) + 8*a(n7)  a(n8) for n>7.
(End)


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 *)


PROG

(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


CROSSREFS

Sequence in context: A256802 A199532 A165004 * A173952 A239422 A165008
Adjacent sequences: A244864 A244865 A244866 * A244868 A244869 A244870


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Jul 07 2014


STATUS

approved



