A268304 Odd numbers n such that binomial(6*n, 2*n) == -1 (mod 8).
1, 5, 21, 73, 85, 273, 293, 297, 329, 341, 529, 545, 1041, 1057, 1089, 1093, 1105, 1173, 1189, 1193, 1297, 1317, 1321, 1353, 1365, 2065, 2081, 2113, 2117, 2129, 2177, 2181, 2209, 2577, 2593, 4113, 4129, 4161, 4165, 4177, 4225, 4229, 4257, 4353, 4357, 4373, 4417, 4421, 4433
Offset: 1
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
- Marc Chamberland and Karl Dilcher, A Binomial Sum Related to Wolstenholme's Theorem, J. Number Theory, Vol. 171, Issue 11 (Nov. 2009), pp. 2659-2672. See Table 2 p. 2669.
Programs
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Mathematica
Select[Range[1, 5000, 2], Mod[Binomial[6 #, 2 #], 8] == 7 &] (* Michael De Vlieger, Feb 07 2016 *)
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PARI
isok(n) = (n%2) && Mod(binomial(6*n, 2*n), 8) == Mod(-1, 8);
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Python
from _future_ import division A268304_list, b, m1, m2 = [], 15, [21941965946880, -54854914867200, 49244258396160, -19011472727040, 2933960577120, -126898662960, 771887070, 385943535, 385945560], [10569646080, -25763512320, 22419210240, -8309145600, 1209116160, -46992960, 415800, 311850, 311850] for n in range(10**3): if b % 8 == 7: A268304_list.append(2*n+1) b = b*m1[-1]//m2[-1] for i in range(8): m1[i+1] += m1[i] m2[i+1] += m2[i] # Chai Wah Wu, Feb 05 2016
Comments