A145995 a(n) = 8 - 12*n + 5*n^2.

1, 4, 17, 40, 73, 116, 169, 232, 305, 388, 481, 584, 697, 820, 953, 1096, 1249, 1412, 1585, 1768, 1961, 2164, 2377, 2600, 2833, 3076, 3329, 3592, 3865, 4148, 4441, 4744, 5057, 5380, 5713, 6056, 6409, 6772, 7145, 7528, 7921, 8324, 8737, 9160, 9593, 10036

Offset

1,2

Comments

For n > 1, a(n) is square if and only if n-1 is in A081016.

a(n) and a(-n) give all numbers m such that 5*m-4 is a square. - Bruno Berselli, Feb 03 2016

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = a(n-1) + 10*n - 17, with a(1)=1. - Vincenzo Librandi, Nov 26 2010

From G. C. Greubel, Jan 30 2016 (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3, a(1)=1, a(2)=4, a(3)=17.

G.f.: x*(1 + x + 8*x^2)/(1-x)^3.

E.g.f.: (5*x^2 - 7*x + 8)*exp(x) - 8. (End)

Example

A081016(0) = 1 and a(2) = 2^2 = 4; A081016(1) = 6 and a(7) = 13^2 = 169; A081016(2) = 40 and a(41) = 89^2 = 7921; A081016(3) = 273 and a(274) = 610^2 = 372100; A081016(4) = 1870 and a(1871) = 4181^2 = 17480761. - Klaus Brockhaus, Oct 29 2008

Mathematica

Table[8 -12x +5x^2, {x, 50}]
s = 1; lst = {s}; Do[s += n + 2; AppendTo[lst, s], {n, 1, 450, 10}]; lst (* Zerinvary Lajos, Jul 11 2009 *)
LinearRecurrence[{3, -3, 1}, {1, 4, 17}, 51] (* G. C. Greubel, Jan 30 2016 *)

Prog

(PARI) for(n=1, 50, print1(8-12*n+5*n^2, ", ")) \\ Klaus Brockhaus, Oct 29 2008
(Magma) [8-12*n+5*n^2: n in [1..50]]; // G. C. Greubel, Jul 15 2019
(Sage) [8-12*n+5*n^2 for n in (1..50)] # G. C. Greubel, Jul 15 2019
(GAP) List([1..50], n-> 8-12*n+5*n^2); # G. C. Greubel, Jul 15 2019

Crossrefs

Cf. A081016, A000217, A080855.

Cf. A195162 (numbers m such that 5*m+4 is a square).

Sequence in context: A041859 A022266 A273309 * A275815 A018973 A212575

Adjacent sequences: A145992 A145993 A145994 * A145996 A145997 A145998

Keyword

nonn,easy

Author

Artur Jasinski, Oct 26 2008

Extensions

Corrected definition; corrected comment; added keyword. - Klaus Brockhaus, Oct 29 2008

Status

approved