A124747
Inverse of number triangle A124744.
Original entry on oeis.org
1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 1, 0, 0, 3, 3, 3, 2, 1, 0, 0, 7, 7, 7, 5, 3, 1, 0, 0, 12, 12, 12, 9, 6, 3, 1, 0, 0, 30, 30, 30, 23, 16, 9, 4, 1, 0, 0, 55, 55, 55, 43, 31, 19, 10, 4, 1
Offset: 0
Triangle begins
1,
0, 1,
0, 0, 1,
0, 0, 1, 1,
0, 0, 1, 1, 1,
0, 0, 2, 2, 2, 1,
0, 0, 3, 3, 3, 2, 1,
0, 0, 7, 7, 7, 5, 3, 1,
0, 0, 12, 12, 12, 9, 6, 3, 1
A124745
Expansion of (1+x)/(1-x^2+x^3).
Original entry on oeis.org
1, 1, 1, 0, 0, -1, 0, -1, 1, -1, 2, -2, 3, -4, 5, -7, 9, -12, 16, -21, 28, -37, 49, -65, 86, -114, 151, -200, 265, -351, 465, -616, 816, -1081, 1432, -1897, 2513, -3329, 4410, -5842, 7739, -10252, 13581, -17991, 23833, -31572, 41824, -55405, 73396, -97229, 128801
Offset: 0
- Paolo Xausa, Table of n, a(n) for n = 0..1000
- Yuksel Soykan, Vedat Irge, and Erkan Tasdemir, A Comprehensive Study of K-Circulant Matrices Derived from Generalized Padovan Numbers, Asian Journal of Probability and Statistics 26 (12):152-70, (2024). See p. 154.
- Index entries for linear recurrences with constant coefficients, signature (0,1,-1).
-
LinearRecurrence[{0, 1, -1}, {1, 1, 1}, 100] (* Paolo Xausa, Aug 27 2024 *)
A124746
Expansion of (1+x^2)/(1-x^4+x^5).
Original entry on oeis.org
1, 0, 1, 0, 1, -1, 1, -1, 1, -2, 2, -2, 2, -3, 4, -4, 4, -5, 7, -8, 8, -9, 12, -15, 16, -17, 21, -27, 31, -33, 38, -48, 58, -64, 71, -86, 106, -122, 135, -157, 192, -228, 257, -292, 349, -420, 485, -549, 641, -769, 905, -1034, 1190, -1410, 1674, -1939, 2224, -2600
Offset: 0
-
LinearRecurrence[{0, 0, 0, 1, -1}, {1, 0, 1, 0, 1}, 100] (* Paolo Xausa, Aug 27 2024 *)
A124749
Expansion of (1+x*y+x^2*y^2)/(1-x^3*y^3+x^4*y^3).
Original entry on oeis.org
1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -3, 1
Offset: 0
Triangle begins
1,
0, 1,
0, 0, 1,
0, 0, 0, 1,
0, 0, 0, -1, 1,
0, 0, 0, 0, -1, 1,
0, 0, 0, 0, 0, -1, 1,
0, 0, 0, 0, 0, 0, -2, 1,
0, 0, 0, 0, 0, 0, 1, -2, 1,
0, 0, 0, 0, 0, 0, 0, 1, -2, 1,
0, 0, 0, 0, 0, 0, 0, 0, 1, -3, 1
Showing 1-4 of 4 results.
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