A125196 Number of magic labelings of the Petersen graph with magic sum n.

1, 6, 27, 87, 228, 513, 1034, 1914, 3315, 5440, 8541, 12921, 18942, 27027, 37668, 51428, 68949, 90954, 118255, 151755, 192456, 241461, 299982, 369342, 450983, 546468, 657489, 785869, 933570, 1102695, 1295496

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]

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

Formula

a(n) = (1/32)*(29*C(n+5,5) + 21*C(n+4,5) + 126*C(n+3,5) - 34*C(n+2,5) + 21*C(n+1,5) - 3*C(n,5) + 3*(-1)^n). [Stanley]. - N. J. A. Sloane, Jul 07 2014

G.f.: (x^4+x^3+6x^2+x+1)/((1-x)^6*(1+x)) [Stanley; Ahmed].

Maple

a := proc(r) local r1 ; r1 := r^5/24+5*r^4/16+25*r^3/24+15*r^2/8+23*r/12 ; if r mod 2 = 0 then r1+1 ; else r1+13/16 ; fi ; end: for n from 0 to 30 do printf("%d ", a(n)) ; od;

Mathematica

CoefficientList[Series[(x^4 + x^3 + 6x^2 + x + 1)/(1 - x)^6/(1 + x), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 12 2012 *)

Crossrefs

Sequence in context: A250283 A100188 A131985 * A100189 A052267 A038166

Adjacent sequences: A125193 A125194 A125195 * A125197 A125198 A125199

Keyword

easy,nonn

Author

R. J. Mathar, Jan 25 2007

Extensions

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

Status

approved