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Search: id:A108243
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| A108243 |
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a(n) = number of 3-Regular (trivalent) multi-graphs without loops on 2n vertices a(n)= number of symmetric 2n X 2n matrices with {0,1,2,3}-entries with row sum equal to 3 for each row and trace 0. |
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4
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| 1, 1, 10, 760, 190050, 103050570, 102359800620, 168076482974400, 424343374430075100, 1560473478516337885500, 8014685021084051980870200, 55595731825871742484530751200, 506777617936508379069463525671000
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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Linear differential equation satisfied by exponential generating function: {D(F)(0) = 1, (41580*t^5-3780*t^4+120*t^2+33*t-3)*F(t)+(498960*t^6-162540*t^5-11340*t^4+3+1350*t^3-60*t+132*t^2)*(diff(F(t), t))+(831600*t^7-466200*t^6-30240*t^5+7410*t^4+44*t^3-81*t^2)*(diff(diff(F(t), t), t))+(443520*t^8-352800*t^7-18144*t^6+7372*t^5-18*t^3)*(diff(diff(diff(F(t), t), t), t))+(95040*t^9-97920*t^8-3456*t^7+1992*t^6)*(diff(diff(diff(diff(F(t), t), t), t), t))+(8448*t^10-10688*t^9-192*t^8+144*t^7)*(diff(diff(diff(diff(diff(F(t), t), t), t), t), t))+(256*t^11-384*t^10)*(diff(diff(diff(diff(diff(diff(F(t), t), t), t), t), t), t)),
with F(0) = 1, `@@`(D, 5)(F)(0) = 103050570, `@@`(D, 2)(F)(0) = 10, `@@`(D, 3)(F)(0) = 760, `@@`(D, 4)(F)(0) = 190050}
Linear recurrence satisfied by a(n): {(4989600 + 5718768*n^7 + 1045440*n^8 + 123200*n^9 + 8448*n^10 + 256*n^11 + 30135960*n + 75458988*n^2 + 105258076*n^3 + 91991460*n^4 + 53358140*n^5 + 21100464*n^6)*a(n) + ( - 19958400 - 1534368*n^7 - 182592*n^8 - 12608*n^9 - 384*n^10 - 75637440*n - 125414712*n^2 - 119890252*n^3 - 73239888*n^4 - 29906772*n^5 - 8276184*n^6)*a(n + 1) + ( - 4989600 - 5760*n^7 - 192*n^8 - 11840760*n - 12084468*n^2 - 6932520*n^3 - 2446668*n^4 - 544320*n^5 - 74592*n^6)*a(n + 2) + (1857240 + 144*n^7 + 3447358*n + 2724762*n^2 + 1186966*n^3 + 307470*n^4 + 47332*n^5 + 4008*n^6)*a(n + 3) + (5445 + 3289*n + 660*n^2 + 44*n^3)*a(n + 4) + ( - 3003 - 1635*n - 297*n^2 - 18*n^3)*a(n + 5) + 3*a(n + 6),
with a(0) = 1, a(1) = 1, a(2) = 10, a(3) = 760, a(4) = 190050, a(5) = 103050570}
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EXAMPLE
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a(1)=1 is the graph on 1, 2 with three copies of the edge (1,2)
a(2)=10 are relabelings of the graphs on 1,2,3,4:
K_4 x 1
+ {(1,2), (1,2), (1,3), (3,4), (3,4), (2,4)} x 6 relabelings
+ {(1,2), (1,2), (1,2), (3,4), (3,4), (3,4)} x 3 relabelings.
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CROSSREFS
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Sequence in context: A117257 A030979 A108247 this_sequence A159709 A015057 A006440
Adjacent sequences: A108240 A108241 A108242 this_sequence A108244 A108245 A108246
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KEYWORD
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nonn
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AUTHOR
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Marni Mishna (marni.mishna(AT)inria.fr), Jun 17 2005
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EXTENSIONS
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Definition corrected by Brendan McKay, Apr 02 2007
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