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A126862
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Numbers n that have a component C(1,1) when expanded in the binomial basis of order t=3.
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0
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3, 6, 8, 12, 14, 17, 22, 24, 27, 31, 37, 39, 42, 46, 51, 58, 60, 63, 67, 72, 78, 86, 88, 91, 95, 100, 106, 113, 122, 124, 127, 131, 136, 142, 149, 157, 167, 169, 172, 176, 181, 187, 194, 202, 211, 222, 224, 227, 231, 236, 242, 249, 257, 266, 276, 288, 290, 293, 297
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OFFSET
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1,1
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COMMENTS
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Each positive integer n has a unique binomial expansion n = C(n_t,t) + C(n_{t-1},t-1) + ... + C(n_v,v) for a given order t, where n_t > n_{t-1} > ... > n_v >= v >= 1. The sequence contains those n for which v=1 and n_v=1 at t=3. The equivalent sequence for t=2 is A000124.
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LINKS
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EXAMPLE
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Expansions in t=3 for n=19 up to 23 are n=19=C(5,3)+C(4,2)+C(3,1);
n=20=C(6,3); n=21=C(6,3)+C(2,2); n=22=C(6,3)+C(2,2)+C(1,1); n=23=C(6,3)+C(3,2).
Of these, only n=22 has a C(1,1) component and makes it into the sequence.
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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