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Search: id:A110041
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| A110041 |
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a(n) = number of labeled graphs on n vertices (with no isolated vertices, multi-edges or loops) such that the degree of every vertex is either of degree at most 3. |
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3
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| 1, 0, 1, 4, 41, 512, 8285, 166582, 4054953, 116797432, 3912076929, 150190759240, 6532014077809, 318632936830136, 17286883399233149, 1035508343364348938
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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P-recursive
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FORMULA
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Linear recurrence satisfied by the sequence: {a(1) = 0, ( - 150917976*n^2 - 105258076*n^3 - 1925*n^9 - 13339535*n^5 - 45995730*n^4 - 357423*n^7 - 2637558*n^6 - 120543840*n - n^11 - 66*n^10 - 39916800 - 32670*n^8)*a(n) + (22057180*n^4 + 2*n^10 + 69934280*n^3 + 140581872*n^2 + 161254080*n + 4621890*n^5 + 79833600 + 130*n^9 + 3720*n^8 + 61620*n^7 + 653226*n^6)*a(n + 1) + (3*n^10 + 6932835*n^5 + 5580*n^8 + 92430*n^7 + 979839*n^6 + 241881120*n + 33085770*n^4 + 104901420*n^3 + 210872808*n^2 + 119750400 + 195*n^9)*a(n + 2) + (6932520*n^3 + 39916800 + 136080*n^5 + 24168936*n^2 + 9324*n^6 + 47363040*n + 1223334*n^4 + 6*n^8 + 360*n^7)*a(n + 3) + (6*n^8 + 1431654*n^4 + 372*n^7 + 9996*n^6 + 152040*n^5 + 59875200 + 8545908*n^3 + 31580424*n^2 + 66054960*n)*a(n + 4) + (9100956*n + 6*n^7 + 9646560 + 3631220*n^2 + 335*n^6 + 7929*n^5 + 103085*n^4 + 794709*n^3)*a(n + 5) + (492*n^6 + 9*n^7 + 11032560 + 11359*n^5 + 143385*n^4 + 1067026*n^3 + 4671483*n^2 + 11110486*n)*a(n + 6) + (1021680 + 1041*n^4 + 17838*n^3 + 150699*n^2 + 626358*n + 24*n^5)*a(n + 7) + (461340 + 7027*n^3 + 9*n^5 + 61461*n^2 + 267044*n + 399*n^4)*a(n + 8) + (100980 + 5751*n^2 + 9*n^4 + 39408*n + 372*n^3)*a(n + 9) + ( - 6414*n - 588*n^2 - 18*n^3 - 23364)*a(n + 10) + ( - 48*n - 528)*a(n + 11) + 24*a(n + 12), a(0) = 1, a(2) = 1, a(3) = 4, a(4) = 41, a(5) = 512, a(6) = 8285, a(7) = 166582, a(8) = 4054953, a(9) = 116797432, a(10) = 3912076929, a(11) = 150190759240}
Differential equation satisfied by the exponential generating function: {F(0) = 1, 9*t^4*(t^4 + t + t^2 - 2)^2*diff(diff(F(t), t), t) + 3*t*( - 4*t^6 + 8*t^5 - 16*t + t^10 - 16*t^2 + 2*t^7 + 8 - 2*t^4 + 2*t^8 + 10*t^3)*(t^4 + t + t^2 - 2)*diff(F(t), t) - t^2*(t^4 + t + t^2 - 2)*(t^10 - 2*t^9 - 6*t^7 - 12*t^6 + t^5 - t^4 + 39*t^3 - 10*t^2 + 24)*F(t)}
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EXAMPLE
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Graphs listed by edgeset
a(3)=4: {(1,2), (2,3)}, {(1,3), (2,3)}, {(1,3), (1,2)}, {(2,3), (1,2), (1,3)}
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CROSSREFS
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Cf. A110040, A110039, A002829, A001205, A001147.
Sequence in context: A114467 A118450 A024383 this_sequence A064327 A134277 A085340
Adjacent sequences: A110038 A110039 A110040 this_sequence A110042 A110043 A110044
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KEYWORD
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easy,nonn
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AUTHOR
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Marni Mishna (marni.mishna(AT)inria.fr), Jul 08 2005
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