OFFSET
0,3
COMMENTS
Binomial transform of A054569 (with leading 0). Partial sums of A014477 (with leading 0). - Paul Barry, Jun 11 2003
This sequence is related to A000337 by a(n) = n*A000337(n) - Sum_{i=0..n-1} A000337(i). - Bruno Berselli, Mar 06 2012
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-18,20,-8).
FORMULA
From Paul Barry, Jun 11 2003: (Start)
G.f.: x*(1+2*x)/((1-x)*(1-2*x)^3).
a(n) = 2^n*(n^2-2*n+3) - 3.
a(n) = Sum_{k=0..n} k^2*2^(k-1). (End)
a(n) = 7*a(n-1) -18*a(n-2) +20*a(n-3) -8*a(n-4). - Harvey P. Dale, Mar 04 2015
E.g.f.: -3*exp(x) + (3 -2*x +4*x^2)*exp(2*x). - G. C. Greubel, Mar 31 2021
MAPLE
MATHEMATICA
LinearRecurrence[{7, -18, 20, -8}, {0, 1, 9, 45}, 29] (* Bruno Berselli, Mar 06 2012 *)
PROG
(Magma) m:=28; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!((1+2*x)/((1-x)*(1-2*x)^3))); // Bruno Berselli, Mar 06 2012
(PARI) for(n=0, 28, print1(2^n*(n^2-2*n+3)-3", ")); \\ Bruno Berselli, Mar 06 2012
(Sage) [2^n*(3-2*n+n^2) -3 for n in (0..30)] # G. C. Greubel, Mar 31 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved