0,6

P-recursive

Marni Mishna, Maple worksheet

Differential equation satisfied by exponential generating function: {F(0) = 1, 36*t^2*(t + 1)*(t^2 - 2)^2*(3*t^2 + 2*t - 2)^2*(diff(diff(F(t), t), t)) - 12*(t + 1)*(3*t^2 + 2*t - 2)*(3*t^10 + 2*t^9 - 8*t^8 - 40*t^7 - 56*t^6 + 4*t^5 - 48*t^4 - 96*t^3 + 80*t^2 + 80*t - 32)*(diff(F(t), t)) + t^3*(t + 1)*(3*t^2 + 2*t - 2)*(3*t^9 + 2*t^8 - 2*t^7 - 108*t^6 - 144*t^5 + 32*t^4 - 24*t^3 + 16*t^2 + 112*t - 64)*F(t)}.

Linear recurrence for a(n): initial values: a(2) = 0, a(3) = 0, a(0) = 1, a(1) = 0, a(4) = 1, a(5) = 12, a(6) = 330, a(7) = 11205, a(8) = 505505, a(9) = 28787052, a(10) = 2024844444, a(11) = 172592502570, a(12) = 17545270969545;

then (1971620508*n^4 + 4242044664*n^3 + 3*n^12 + 4459328640*n + 1437004800 +

167310*n^9 + 5794678656*n^2 + 20779902*n^7 + 234*n^11 + 8151*n^10 + 2248389*n^8

+ 618210450*n^5 + 134970693*n^6)*a(n) + (154*n^10 + 77519860*n^5 + 334620440*n^4

+ 958003200 + 5280*n^9 + 106260*n^8 + 1392666*n^7 + 12460602*n^6 + 979793232*n^3

+ 1848236544*n^2 + 2014882560*n + 2*n^11)*a(n + 1) + ( - 96300*n^7 - 1200066*n^6

- 540148032*n^2 - 767940480*n - 4980*n^8 - 57398920*n^4 - 219822600*n^3

- 479001600 - 10060470*n^5 - 2*n^10 - 150*n^9)*a(n + 2) + ( - 97416*n^8

- 17244057600 - 24771847680*n - 2808*n^9 - 36*n^10 - 1978992*n^7 - 26064612*n^6

- 232501752*n^5 - 1422206064*n^4 - 5889271968*n^3 - 15795689472*n^2)*a(n

+ 3) + ( - 5364230400*n - 4790016000 - 24*n^9 - 1872*n^8 - 64368*n^7 - 1280160*n^6

- 16223256*n^5 - 135808848*n^4 - 750702432*n^3 - 2641118400*n^2)*a(n + 4)

+ (3252704*n^5 + 2043740160 + 194208*n^6 + 2058817536*n + 33702144*n^4 +

221164160*n^3 + 897495552*n^2 + 6560*n^7 + 96*n^8)*a(n + 5) + (246432*n^6

+ 48931572*n^4 + 4055546880 + 1512709248*n^2 + 4406952*n^5 + 7824*n^7 +

345350856*n^3 + 108*n^8 + 3758813568*n)*a(n + 6) + (528439296*n + 2696360*n^4

+ 27036368*n^3 + 161115712*n^2 + 159784*n^5 + 5208*n^6 + 72*n^7 + 735989760)*a(n

+ 7) + ( - 59595808*n^2 - 8517816*n^3 - 338532480 - 504*n^6 - 680168*n^4

- 220837728*n - 28776*n^5)*a(n + 8) + ( - 262432*n^3 - 288*n^5 - 11355392*n

- 13824*n^4 - 20613120 - 2459328*n^2)*a(n + 9) + (31392*n^3 + 3713184*n

+ 720*n^4 + 512496*n^2 + 10074240)*a(n + 10) + (253440 + 288*n^3 + 8544*n^2

+ 82176*n)*a(n + 11) + ( - 7584*n - 49536 - 288*n^2)*a(n + 12) + 384*a(n + 13).

The 3-regular 3-hypergraphs on 4 vertices: {1,2,3}, {2,3,4},{3,4,1},{4,1,2}

Cf. A025035, A110100, A002829.

Sequence in context: A083431 A080141 A153468 this_sequence A009530 A159363 A009680

Adjacent sequences: A110098 A110099 A110100 this_sequence A110102 A110103 A110104

easy,nonn

Marni Mishna (marni.mishna(AT)inria.fr), Jul 11 2005