A131098 Partial sums of A151798.

1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179, 183, 187, 191, 195, 199, 203, 207, 211, 215, 219, 223, 227, 231, 235, 239

Offset

1,2

Comments

1 together with A004767. - Omar E. Pol, Feb 23 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

David Applegate, The movie version

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(1) = 1, a(n) = 4*n - 5 for n >= 2. - Jaroslav Krizek, Aug 15 2009

G.f.: x*(x+2*x^2+1)/(x-1)^2. - R. J. Mathar, Dec 08 2010

E.g.f.: exp(x)*(4*x - 5) + 5 + 2*x. - Stefano Spezia, Mar 21 2025

Example

g.f. = x + 3*x^2 + 7*x^3 + 11*x^4 + 15*x^5 + 19*x^6 + 23*x^7 + 27*x^8 + ...

Mathematica

CoefficientList[Series[(x + 2 x^2 + 1)/(x - 1)^2, {x, 0, 80}], x] (* Vincenzo Librandi, Feb 25 2014 *)
LinearRecurrence[{2, -1}, {1, 3, 7}, 70] (* Harvey P. Dale, Jan 03 2023 *)

Prog

(Magma) I:=[1, 3, 7]; [n le 3 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..70]]; // Vincenzo Librandi, Feb 25 2014
(PARI) A131098(n)=abs(4*n-5) \\ M. F. Hasler, Apr 27 2018

Crossrefs

Cf. A151798, A004767.

Sequence in context: A172338 A189787 A004767 * A334228 A118894 A194397

Adjacent sequences: A131095 A131096 A131097 * A131099 A131100 A131101

Keyword

nonn,easy

Author

Hans Isdahl, Sep 24 2007

Extensions

Edited by N. J. A. Sloane, Jun 29 2009

Status

approved