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

Author

Matt C. Anderson, Sep 09 2014

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A002522, A001105.

Programs

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 *)

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

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)

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.