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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
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