A036826 a(n) = A036800(n)/2.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000337, A014477, A036800, A054569, A209359.

Programs

Magma

m:=28; R:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!((1+2*x)/((1-x)*(1-2*x)^3))); // Bruno Berselli, Mar 06 2012

Maple

A036826:= n-> 2^n*(3-2*n+n^2) -3; seq(A036826(n), n=0..30); # G. C. Greubel, Mar 31 2021

Mathematica

LinearRecurrence[{7,-18,20,-8}, {0,1,9,45}, 29] (* 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

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