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
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