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

Author

Artur Jasinski, Oct 26 2008

Keywords

• nonn
• easy

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

Examples

			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
		

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).

Crossrefs

Cf. A081016, A000217, A080855.

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

Programs

GAP

List([1..50], n-> 8-12*n+5*n^2); # G. C. Greubel, Jul 15 2019

Magma

[8-12*n+5*n^2: n in [1..50]]; // G. C. Greubel, Jul 15 2019

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 *)

PARI

for(n=1, 50, print1(8-12*n+5*n^2, ",")) \\ Klaus Brockhaus, Oct 29 2008

Sage

[8-12*n+5*n^2 for n in (1..50)] # G. C. Greubel, Jul 15 2019

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)

Extensions

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