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A125196
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Number of magic labelings of the Petersen graph with magic sum n.
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1
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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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].
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MAPLE
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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;
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MATHEMATICA
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CoefficientList[Series[(x^4 + x^3 + 6x^2 + x + 1)/(1 - x)^6/(1 + x), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 12 2012 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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