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A183225 Array: row r is the complement of the (r+2)-gonal numbers; by antidiagonals.

%I A183225 #16 Oct 07 2024 01:18:24
%S A183225 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,
%T A183225 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,
%U A183225 4,3,2,17,14,13,11,10,9,7,6,5,4,3,2,18
%N A183225 Array:  row r is the complement of the (r+2)-gonal numbers; by antidiagonals.
%C A183225 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
%H A183225 Chai Wah Wu, <a href="/A183225/b183225.txt">Table of n, a(n) for n = 1..10000</a>
%e A183225 Northwest corner:
%e A183225 2...4...5...7...8...9...11...12...13 (A014132)
%e A183225 2...3...5...6...7...8...10...11...12 (A000037)
%e A183225 2...3...4...6...7...8....9...10...11 (A183217)
%e A183225 2...3...4...5...7...8....9...10...11 (A183218)
%e A183225 2...3...4...5...6...8....9...10...11 (A183219)
%e A183225 2...3...4...5...6...7....9...10...11 (A183220)
%e A183225 2...3...4...5...6...7....8...10...11 (A183221)
%o A183225 (Python)
%o A183225 from itertools import count, islice
%o A183225 from math import isqrt
%o A183225 def A183225_T(n,k): return n+(isqrt(((n<<3)+(-8+(k+1&-4) if k>10 else 0))//(k-2))+1>>1)
%o A183225 def A183225_gen(): # generator of terms
%o A183225     return (A183225_T(m-k+3,k) for m in count(1) for k in range(3,m+3))
%o A183225 A183225_list = list(islice(A183225_gen(),100)) # _Chai Wah Wu_, Oct 06 2024
%Y A183225 Cf. A086270 (array of the r-gonal numbers by rows),
%Y A183225 A014132 (complement of the triangular numbers),
%Y A183225 A000037 (complement of the squares),
%Y A183225 A183217 (complement of the pentagonal numbers).
%K A183225 nonn,tabl
%O A183225 1,1
%A A183225 _Clark Kimberling_, Jan 01 2011