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A350090
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a(n) is the number of indices i in the range 0 <= i <= n-1 such that A003215(n) - A003215(i) is an oblong number (A002378), where A003215 are the hex numbers.
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4
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0, 1, 1, 1, 1, 3, 1, 2, 3, 1, 1, 1, 3, 1, 1, 3, 3, 1, 3, 3, 3, 3, 5, 1, 1, 1, 5, 1, 1, 3, 1, 3, 1, 7, 1, 3, 3, 1, 1, 3, 7, 1, 1, 3, 3, 1, 3, 3, 1, 1, 3, 3, 1, 3, 7, 1, 3, 7, 1, 7, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 7, 5, 3, 3, 1, 5, 3, 3, 7, 3, 1, 1, 3, 3, 3, 7, 1, 3, 1, 3, 1
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OFFSET
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0,6
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COMMENTS
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There are very few even terms in the data (3 up to 10000). They are obtained for indices coming from A001921. For odd terms see A350120.
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LINKS
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FORMULA
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EXAMPLE
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For n=5, the 5 numbers hex(5)-hex(i), for i=0 to 4, are (90, 84, 72, 54, 30) out of which 90, 72 and 30 are oblong, so a(5) = 3.
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MATHEMATICA
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obQ[n_] := IntegerQ @ Sqrt[4*n + 1]; hex[n_] := 3*n*(n + 1) + 1; a[n_] := Module[{h = hex[n]}, Count[Range[0, n - 1], _?(obQ[h - hex[#]] &)]]; Array[a, 100, 0] (* Amiram Eldar, Dec 14 2021 *)
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PROG
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(PARI) hex(n) = 3*n*(n+1)+1; \\ A003215
isob(n) = my(m=sqrtint(n)); m*(m+1)==n; \\ A002378
a(n) = my(h=hex(n)); sum(k=0, n-1, isob(h - hex(k)));
(PARI) a(n) = numdiv(3*n*n + 3*n + 1) - 1; \\ Jinyuan Wang, Dec 19 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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