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

Author

Hans Isdahl, Sep 24 2007

Keywords

• nonn
• easy

Comments

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

Examples

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

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).

Crossrefs

Cf. A151798, A004767.

Programs

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

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 *)

PARI

A131098(n)=abs(4*n-5) \\ M. F. Hasler, Apr 27 2018

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

Extensions

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