A247018 Numbers of the form 3*z^2 + z + 3 for some integer z.

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

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

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

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

Cf. A002522, A001105.

Sequence in context: A137270 A071111 A177070 * A038929 A242755 A070806

Adjacent sequences: A247015 A247016 A247017 * A247019 A247020 A247021

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