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(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
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Nov 21 2009
STATUS
approved