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A350090 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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
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.
a(n) = 1 for n in A111251.
LINKS
FORMULA
a(n) = A000005(A003215(n)) - 1. - Jinyuan Wang, Dec 19 2021
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Cf. also A001921, A111251, A350120.
Sequence in context: A125061 A163746 A004591 * A195588 A153510 A288537
KEYWORD
nonn
AUTHOR
Klaus Purath and Michel Marcus, Dec 14 2021
EXTENSIONS
Edited by N. J. A. Sloane, Dec 25 2021
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)