A125198 Number of magical labelings of the octahedral graph of magic sum n.

1, 8, 40, 144, 417, 1032, 2272, 4568, 8545, 15072, 25320, 40824, 63553, 95984, 141184, 202896, 285633, 394776, 536680, 718784, 949729, 1239480, 1599456, 2042664, 2583841, 3239600, 4028584, 4971624, 6091905, 7415136, 8969728, 10786976, 12901249, 15350184

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

M. M. Ahmed, Algebraic Combinatorics of Magic Squares, math.CO/0405476, p73.

R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]

Index entries for linear recurrences with constant coefficients, signature (6,-14,14,0,-14,14,-6,1).

Formula

G.f.: (1+2*x+6*x^2+2*x^3+x^4)/((1-x)^7*(1+x)). [Stanley] - N. J. A. Sloane, Jul 07 2014

From Colin Barker, Jan 13 2017: (Start)

a(n) = (15*(31+(-1)^n) + 1152*n + 1216*n^2 + 720*n^3 + 250*n^4 + 48*n^5 + 4*n^6) / 480.

a(n) = 6*a(n-1) - 14*a(n-2) + 14*a(n-3) - 14*a(n-5) + 14*a(n-6) - 6*a(n-7) + a(n-8) for n>7.

(End)

Maple

a := proc(r) local r2 ; r2 := r^6/120+r^5/10+25*r^4/48+3*r^3/2+38*r^2/15+12*r/5 ; if r mod 2 = 0 then r2+1 ; else r2+15/16 ; fi ; end: for n from 0 to 40 do printf("%d ", a(n)) ; od;

Mathematica

(1 + 2*x + 6*x^2 + 2*x^3 + x^4)/((1 - x)^7*(1 + x)) + O[x]^40 // CoefficientList[#, x]& (* Jean-François Alcover, Apr 01 2018 *)

Prog

(PARI) Vec((1+2*x+6*x^2+2*x^3+x^4)/((1-x)^7*(1+x)) + O(x^40)) \\ Colin Barker, Jan 13 2017

Crossrefs

Sequence in context: A191903 A028596 A264602 * A128639 A341365 A004405

Adjacent sequences: A125195 A125196 A125197 * A125199 A125200 A125201

Keyword

easy,nonn

Author

R. J. Mathar, Jan 25 2007

Extensions

Stanley reference added by N. J. A. Sloane, Jul 07 2014

Status

approved