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A036826 A036800/2. 8
0, 1, 9, 45, 173, 573, 1725, 4861, 13053, 33789, 84989, 208893, 503805, 1196029, 2801661, 6488061, 14876669, 33816573, 76283901, 170917885, 380633085, 843055101, 1858076669, 4076863485, 8908701693, 19394461693, 42077257725, 90999619581, 196226318333 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform of A054569 (with leading zero). Partial sums of A014477 (with leading zero). - Paul Barry, Jun 11 2003

This sequence is related to A000337 by a(n) = n*A000337(n)-sum(A000337(i), i=0..n-1). - 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(0)=0, a(1)=1, a(2)=9, a(3)=45, a(n)=7*a(n-1)-18*a(n-2)+ 20*a(n-3)- 8*a(n-4). - Harvey P. Dale, Mar 04 2015

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

CROSSREFS

Cf. A000337, A014477, A054569, A209359.

Sequence in context: A144902 A128643 A276280 * A022574 A321948 A050574

Adjacent sequences:  A036823 A036824 A036825 * A036827 A036828 A036829

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 15 13:20 EST 2019. Contains 329149 sequences. (Running on oeis4.)