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

0,3

Links

Stefano Spezia, Table of n, a(n) for n = 0..1500

Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

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

Example

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).

Mathematica

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

Crossrefs

Cf. A141290.

Sequence in context: A262600 A034577 A372878 * A278027 A225895 A089106

Adjacent sequences: A141288 A141289 A141290 * A141292 A141293 A141294

Keyword

nonn,easy

Author

Gary W. Adamson, Jun 22 2008

Extensions

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

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

Status

approved