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A125198 Number of magical labelings of the octahedral graph of magic sum n. 1
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 (list; graph; refs; listen; history; text; internal format)
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R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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

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Last modified December 2 14:15 EST 2022. Contains 358510 sequences. (Running on oeis4.)