A157659 a(n) = 100*n^2 - n.

99, 398, 897, 1596, 2495, 3594, 4893, 6392, 8091, 9990, 12089, 14388, 16887, 19586, 22485, 25584, 28883, 32382, 36081, 39980, 44079, 48378, 52877, 57576, 62475, 67574, 72873, 78372, 84071, 89970, 96069, 102368, 108867, 115566, 122465, 129564

Offset

1,1

Comments

The identity (200*n - 1)^2 - (100*n^2 - n)*(20)^2 = 1 can be written as A157955(n)^2 - a(n)*(20)^2 = 1 (see Barbeau's paper).

Also, the identity (80000*n^2 - 800*n + 1)^2 - (100*n^2 - n)*(8000*n - 40)^2 = 1 can be written as A157661(n)^2 - a(n)*A157660(n)^2 = 1 (see also the second part of the comment at A157661). - Vincenzo Librandi, Jan 28 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 14 in the first table at p. 85, case d(t) = t*(10^2*t-1)).

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

Formula

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

G.f.: x*(99 + 101*x)/(1-x)^3.

E.g.f.: x*(99 + 100*x)*exp(x). - G. C. Greubel, Nov 17 2018

Mathematica

LinearRecurrence[{3, -3, 1}, {99, 398, 897}, 50]

Prog

(Magma) I:=[99, 398, 897]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n)=100*n^2-n \\ Charles R Greathouse IV, Dec 28 2011
(Sage) [100*n^2-n for n in (1..40)] # G. C. Greubel, Nov 17 2018
(GAP) List([1..40], n -> 100*n^2-n); # G. C. Greubel, Nov 17 2018

Crossrefs

Cf. A157660, A157661, A157995.

Sequence in context: A027579 A304675 A316122 * A273187 A322830 A212779

Adjacent sequences: A157656 A157657 A157658 * A157660 A157661 A157662

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 04 2009

Status

approved