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A094832 Number of (s(0), s(1), ..., s(2n+1)) such that 0 < s(i) < 9 and |s(i) - s(i-1)| = 1 for i = 1,2,...,2n+1, s(0) = 3, s(2n+1) = 4. 5
1, 3, 10, 34, 117, 406, 1417, 4965, 17443, 61390, 216318, 762841, 2691574, 9500193, 33539833, 118428835, 418214706, 1476968554, 5216307805, 18423344550, 65070265609, 229827800509, 811757757123, 2867166603766, 10127007608998 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
In general, a(n) = (2/m)*Sum_{r=1..m-1} 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(i-1)| = 1 for i = 1,2,...,2n+1, s(0) = j, s(2n+1) = k.
LINKS
FORMULA
a(n+1) = 3*a(n) + A094833(n-1). - Philippe Deléham, Mar 18 2007
a(n) = (2/9)*Sum_{r=1..8} sin(r*Pi/3)*sin(4*r*Pi/9)*(2*cos(r*Pi/9))^(2n).
a(n) = 6a(n-1) - 9a(n-2) + a(n-3).
G.f.: (-1+3x-x^2)/(-1+6x-9x^2+x^3).
a(n) = A094833(n+2) - 3*A094833(n+1). - Philippe Deléham, Mar 18 2007
MATHEMATICA
LinearRecurrence[{6, -9, 1}, {1, 3, 10}, 30] (* Harvey P. Dale, May 18 2011 *)
CROSSREFS
Cf. A094833.
Sequence in context: A291292 A289612 A059738 * A217778 A071725 A026016
KEYWORD
nonn
AUTHOR
Herbert Kociemba, Jun 13 2004
STATUS
approved

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Last modified March 29 11:43 EDT 2024. Contains 371278 sequences. (Running on oeis4.)