Original entry on oeis.org
1, 2, 5, 11, 17, 27, 42, 57, 78, 106, 134, 170, 215, 260, 315, 381, 447, 525, 616, 707, 812, 932, 1052, 1188, 1341, 1494, 1665, 1855, 2045, 2255, 2486, 2717, 2970, 3246, 3522, 3822, 4147, 4472, 4823, 5201, 5579, 5985, 6420, 6855, 7320, 7816, 8312, 8840, 9401
Offset: 0
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- B. N. Cyvin et al., Enumeration of conjugated hydrocarbons: Hollow hexagons revisited, Structural Chem., 6 (1995), 85-88, equation (7).
- Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).
-
CoefficientList[Series[(x^3 + 2 x^2 + 1)/((x - 1)^4 (x^2 + x + 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 22 2013 *)
A038391
Expansion of (x^3+2*x+1) / ((x-1)^4*(x^2+x+1)^2).
Original entry on oeis.org
1, 4, 7, 13, 23, 33, 48, 69, 90, 118, 154, 190, 235, 290, 345, 411, 489, 567, 658, 763, 868, 988, 1124, 1260, 1413, 1584, 1755, 1945, 2155, 2365, 2596, 2849, 3102, 3378, 3678, 3978, 4303, 4654, 5005, 5383, 5789, 6195, 6630, 7095, 7560, 8056, 8584, 9112, 9673
Offset: 0
- B. N. Cyvin et al., Enumeration of conjugated hydrocarbons..., Structural Chem., 6 (1995), 85-88, equation (8).
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).
-
CoefficientList[Series[(x^3 + 2 x + 1)/((x - 1)^4 (x^2 + x + 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 22 2013 *)
LinearRecurrence[{2,-1,2,-4,2,-1,2,-1},{1,4,7,13,23,33,48,69},50] (* Harvey P. Dale, Sep 22 2015 *)
A264620
Triangle read by rows: T(n,k) (0 <= k <= n) = number of principal ideals generated by an element of rank k in the 3-tonal partition monoid on n elements.
Original entry on oeis.org
1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 1, 1, 2, 3, 2, 1, 1, 0, 1, 2, 3, 3, 2, 1, 1, 0, 1, 2, 3, 4, 3, 2, 1, 1, 1, 1, 2, 4, 4, 4, 3, 2, 1, 1, 0, 1, 2, 3, 5, 5, 4, 3, 2, 1, 1, 0, 1, 2, 3, 5, 6, 5, 4, 3, 2, 1, 1, 1, 1, 2, 4, 5, 6, 7, 5, 4, 3, 2, 1, 1
Offset: 0
Triangle begins:
1,
0,1,
0,1,1,
1,1,1,1,
0,1,2,1,1,
0,1,2,2,1,1,
1,1,2,3,2,1,1,
0,1,2,3,3,2,1,1,
0,1,2,3,4,3,2,1,1,
1,1,2,4,4,4,3,2,1,1,
0,1,2,3,5,5,4,3,2,1,1,
0,1,2,3,5,6,5,4,3,2,1,1,
1,1,2,4,5,6,7,5,4,3,2,1,1,
...
Showing 1-3 of 3 results.
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