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