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A247018 Numbers of the form 3*z^2 + z + 3 for some integer z. 1
3, 5, 7, 13, 17, 27, 33, 47, 55, 73, 83, 105, 117, 143, 157, 187, 203, 237, 255, 293, 313, 355, 377, 423, 447, 497, 523, 577, 605, 663, 693, 755, 787, 853, 887, 957, 993, 1067, 1105, 1183, 1223, 1305, 1347, 1433, 1477, 1567, 1613, 1707, 1755, 1853, 1903 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Note that z is allowed to be negative. - N. J. A. Sloane, Jul 09 2021
Subsequence of A134407.
Numbers k such that 12*k - 35 is a square. - Robert Israel, Sep 18 2014
LINKS
FORMULA
From Colin Barker, Feb 01 2018: (Start)
G.f.: x*(3 + 2*x - 4*x^2 + 2*x^3 + 3*x^4) / ((1 - x)^3*(1 + x)^2).
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>5. (End)
MAPLE
select(t -> issqr(12*t-35), [$1..1000]); # Robert Israel, Sep 18 2014
MATHEMATICA
Union[Flatten[Table[3z^2+{z, -z}+3, {z, 0, 40}]]] (* or *) LinearRecurrence[ {1, 2, -2, -1, 1}, {3, 5, 7, 13, 17}, 60] (* Harvey P. Dale, Jul 10 2021 *)
PROG
(PARI) Vec(x*(3 + 2*x - 4*x^2 + 2*x^3 + 3*x^4) / ((1 - x)^3*(1 + x)^2) + O(x^60)) \\ Colin Barker, Feb 01 2018
CROSSREFS
Sequence in context: A137270 A071111 A177070 * A038929 A242755 A070806
KEYWORD
nonn,easy
AUTHOR
Matt C. Anderson, Sep 09 2014
EXTENSIONS
At some point in the history of this entry the definition was changed from the correct definition to the erroneous "a(n) = 3*n^2 + n + 3". I have restored the original definition, and I deleted some incorrect programs. Thanks to Harvey P. Dale for pointing out that something was wrong. - N. J. A. Sloane, Jul 09 2021.
STATUS
approved

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)