A268581 a(n) = 2*n^2 + 8*n + 5.

5, 15, 29, 47, 69, 95, 125, 159, 197, 239, 285, 335, 389, 447, 509, 575, 645, 719, 797, 879, 965, 1055, 1149, 1247, 1349, 1455, 1565, 1679, 1797, 1919, 2045, 2175, 2309, 2447, 2589, 2735, 2885, 3039, 3197, 3359, 3525, 3695, 3869, 4047, 4229, 4415, 4605

Offset: 0

Author

Juri-Stepan Gerasimov, Apr 10 2016

Keywords

• nonn
• easy

Comments

Also, numbers m such that 2*m + 6 is a square.

All the terms end with a digit in {5, 7, 9}, or equivalently, are congruent to {5, 7, 9} mod 10. - Stefano Spezia, Aug 05 2021

Links

• Stefano Spezia, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. numbers n such that 2*n + k is a perfect square: A093328 (k=-6), A097080 (k=-5), no sequence (k=-4), A051890 (k=-3), A058331 (k=-2), A001844 (k=-1), A001105 (k=0), A046092 (k=1), A056222 (k=2), A142463 (k=3), A054000 (k=4), A090288 (k=5), this sequence (k=6), A059993 (k=7), A147973 (k=8), A139570 (k=9), no sequence (k=10), A222182 (k=11), A152811 (k=12), A181570 (k=13).

Programs

Magma

[2*n^2+8*n+5: n in [0..60]];

Magma

[n: n in [0..6000] | IsSquare(2*n+6)];

Mathematica

Table[2 n^2 + 8 n + 5, {n, 0, 50}] (* Vincenzo Librandi, Apr 13 2016 *)
LinearRecurrence[{3,-3,1},{5,15,29},50] (* Harvey P. Dale, Jan 18 2017 *)

PARI

lista(nn) = for(n=0, nn, print1(2*n^2+8*n+5, ", ")); \\ Altug Alkan, Apr 10 2016

Sage

[2*n^2 + 8*n + 5 for n in [0..46]] # Stefano Spezia, Aug 04 2021

Formula

From Vincenzo Librandi, Apr 13 2016: (Start)

G.f.: (5-x^2)/(1-x)^3.

a(n) = 2*(n+2)^2 - 3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

E.g.f.: exp(x)*(5 + 10*x + 2*x^2). - Stefano Spezia, Aug 03 2021

Extensions

Changed offset from 1 to 0, adapted formulas and programs by Bruno Berselli, Apr 13 2016