A168251 a(n) = n^2 if n is odd, n^2*2^(n-2) if n is even.

0, 1, 4, 9, 64, 25, 576, 49, 4096, 81, 25600, 121, 147456, 169, 802816, 225, 4194304, 289, 21233664, 361, 104857600, 441, 507510784, 529, 2415919104, 625, 11341398016, 729, 52613349376, 841, 241591910400, 961, 1099511627776, 1089, 4964982194176, 1225

Offset: 0

Author

Paul Curtz, Nov 21 2009

Keywords

• nonn
• easy

Comments

This is the main diagonal of the following array defined by T(n,2k+1) = A168077(k) for odd column indices and T(n,2k) = A168077(2k)*2^n for even column indices:

0, 1, 1, 9, 4, 25, ... A168077

0, 1, 2, 9, 8, 25, ... A129194

0, 1, 4, 9, 16,25, ... A000290

0, 1, 8, 9, 32,25, ...

0, 1, 16,9, 64,25, ... A154615

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0, 15, 0, -87, 0, 245, 0, -348, 0, 240, 0, -64).

Programs

Magma

[(n^2)*2^((n-2)*(1+(-1)^n) div 2): n in [0..40]]; // Vincenzo Librandi, Jul 17 2016

Maple

A168251 := proc(n)
        if type(n,'even') then
                n^2*2^n/4 ;
        else
                n^2 ;
        end if;
end proc: # R. J. Mathar, Sep 20 2011

Mathematica

Table[(n^2)*2^((n - 2)*(1 + (-1)^n)/2), {n, 0, 50}] (* G. C. Greubel, Jul 16 2016 *)
Table[If[OddQ[n],n^2,n^2 2^(n-2)],{n,0,50}] (* or *) LinearRecurrence[{0,15,0,-87,0,245,0,-348,0,240,0,-64},{0,1,4,9,64,25,576,49,4096,81,25600,121},41] (* Harvey P. Dale, May 14 2022 *)

Formula

a(2n) = A128782(n). a(2n+1) = A016754(n).

a(n) = +15*a(n-2) -87*a(n-4) +245*a(n-6) -348*a(n-8) +240*a(n-10) - 64*a(n-12).

G.f.: x*(1 + 4*x - 6*x^2 + 4*x^3 - 23*x^4 - 36*x^5 + 212*x^6 + 44*x^7 - 336*x^8 - 16*x^9 - 64*x^10) / ( (1-x)^3*(2*x+1)^3*(1-2*x)^3*(1+x)^3 ). - R. J. Mathar, Sep 20 2011

a(n) = (n^2)*2^((n-2)*(1+(-1)^n)/2). - Luce ETIENNE, Feb 03 2015