A141291 a(n) = 4*a(n-1) + 2*n - 1.

0, 1, 7, 33, 139, 565, 2271, 9097, 36403, 145629, 582535, 2330161, 9320667, 37282693, 149130799, 596523225, 2386092931, 9544371757, 38177487063, 152709948289, 610839793195, 2443359172821, 9773436691327, 39093746765353, 156374987061459, 625499948245885, 2501999792983591

Offset: 0

Author

Gary W. Adamson, Jun 22 2008

Keywords

• nonn
• easy

Examples

			a(4) = 139 = 4*a(3) + 7 = 4*33 + 7.
a(4) = 139 = sum of row 4 terms of triangle A141290 = (64, + 48 + 20 + 7).
		

Links

• Stefano Spezia, Table of n, a(n) for n = 0..1500
• Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

Crossrefs

Cf. A141290.

Programs

Mathematica

LinearRecurrence[{6,-9,4},{0,1,7},27] (* Stefano Spezia, May 21 2024 *)

Formula

a(n) = 4*a(n-1) + 2*n-1, given a(0) = 0, a(1) = 1.

Row sums of triangle A141290 starting with offset 1.

From R. J. Mathar, Feb 02 2010: (Start)

a(n) = 6*a(n-1) -9*a(n-2) +4*a(n-3).

G.f.: x*(1+x)/((1-4*x)*(x-1)^2). (End)

E.g.f.: exp(x)*(5*(exp(3*x) - 1) - 6*x) /9. - Stefano Spezia, May 21 2024

Extensions

Definition and formula corrected by Paolo P. Lava, Oct 07 2008

More terms from R. J. Mathar, Feb 02 2010