

A094827


Number of (s(0), s(1), ..., s(2n+1)) such that 0 < s(i) < 9 and s(i)  s(i1) = 1 for i = 1,2,...,2n+1, s(0) = 1, s(2n+1) = 4.


3



1, 4, 14, 48, 165, 571, 1988, 6953, 24396, 85786, 302104, 1064945, 3756519, 13256712, 46796545, 165225380, 583440086, 2060408640, 7276716445, 25700060995, 90770326604, 320598127113, 1132355884236, 3999522488002
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OFFSET

1,2


COMMENTS

In general, a(n) = (2/m)*Sum_{r=1..m1} sin(r*j*Pi/m)*sin(r*k*Pi/m)*(2*cos(r*Pi/m))^(2n+1) counts (s(0), s(1), ..., s(2n+1)) such that 0 < s(i) < m and s(i)  s(i1) = 1 for i = 1,2,...,2n+1, s(0) = j, s(2n+1) = k.


LINKS



FORMULA

a(n) = (2/9)*Sum_{r=1..8} sin(r*Pi/9)*sin(4*r*Pi/9)*(2*cos(r*Pi/9))^(2*n+1).
a(n) = 7*a(n1)  15*a(n2) + 10*a(n3)  a(n4).
G.f.: x*(13*x+x^2) / ( (x1)*(x^39*x^2+6*x1) ).


MATHEMATICA

LinearRecurrence[{7, 15, 10, 1}, {1, 4, 14, 48}, 30] (* Harvey P. Dale, Jul 09 2020 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



