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

0,3

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).

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

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 *)

Prog

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

Crossrefs

Sequence in context: A073658 A059479 A094083 * A062758 A217854 A369866

Adjacent sequences: A168248 A168249 A168250 * A168252 A168253 A168254

Keyword

nonn,easy

Author

Paul Curtz, Nov 21 2009

Status

approved