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A183225
Array: row r is the complement of the (r+2)-gonal numbers; by antidiagonals.
2
2, 4, 2, 5, 3, 2, 7, 5, 3, 2, 8, 6, 4, 3, 2, 9, 7, 6, 4, 3, 2, 11, 8, 7, 5, 4, 3, 2, 12, 10, 8, 7, 5, 4, 3, 2, 13, 11, 9, 8, 6, 5, 4, 3, 2, 14, 12, 10, 9, 8, 6, 5, 4, 3, 2, 16, 13, 11, 10, 9, 7, 6, 5, 4, 3, 2, 17, 14, 13, 11, 10, 9, 7, 6, 5, 4, 3, 2, 18
OFFSET
1,1
COMMENTS
The n-th non k-gonal number is given by n+round(sqrt(2n/(k-2))) for k <= 10 and given by n+round(sqrt((2n-2+floor((k+1)/4))/(k-2))) for k > 10. - Chai Wah Wu, Oct 06 2024
EXAMPLE
Northwest corner:
2...4...5...7...8...9...11...12...13 (A014132)
2...3...5...6...7...8...10...11...12 (A000037)
2...3...4...6...7...8....9...10...11 (A183217)
2...3...4...5...7...8....9...10...11 (A183218)
2...3...4...5...6...8....9...10...11 (A183219)
2...3...4...5...6...7....9...10...11 (A183220)
2...3...4...5...6...7....8...10...11 (A183221)
PROG
(Python)
from itertools import count, islice
from math import isqrt
def A183225_T(n, k): return n+(isqrt(((n<<3)+(-8+(k+1&-4) if k>10 else 0))//(k-2))+1>>1)
def A183225_gen(): # generator of terms
return (A183225_T(m-k+3, k) for m in count(1) for k in range(3, m+3))
A183225_list = list(islice(A183225_gen(), 100)) # Chai Wah Wu, Oct 06 2024
CROSSREFS
Cf. A086270 (array of the r-gonal numbers by rows),
A014132 (complement of the triangular numbers),
A000037 (complement of the squares),
A183217 (complement of the pentagonal numbers).
Sequence in context: A307664 A057037 A076920 * A366586 A020774 A291303
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 01 2011
STATUS
approved