OFFSET
0,2
COMMENTS
a(n) is the number of quads in the EvenQuads-2^{n+2} deck. - Tanya Khovanova and MIT PRIMES STEP senior group, Jul 02 2023
LINKS
T. D. Noe, Table of n, a(n) for n=0..100
Julia Crager, Felicia Flores, Timothy E. Goldberg, Lauren L. Rose, Daniel Rose-Levine, Darrion Thornburgh, and Raphael Walker, How many cards should you lay out in a game of EvenQuads? A detailed study of 2-caps in AG(n,2), arXiv:2212.05353 [math.CO], 2023.
Index entries for linear recurrences with constant coefficients, signature (14,-56,64).
FORMULA
G.f.: 1/((1-2x)*(1-4x)*(1-8x)).
Difference of Gaussian binomial coefficients [ n+1, 3 ] - [ n, 3 ] (n >= 2).
a(n) = (2^n-6*4^n+8*8^n)/3. - James R. Buddenhagen, Dec 14 2003
a(n) = Sum_{0<=i,j,k,<=n; i+j+k=n} 2^i*4^j*8^k. - Hieronymus Fischer, Jun 25 2007
From Vincenzo Librandi, Mar 15 2011: (Start)
a(n) = 14*a(n-1) - 56*a(n-2) + 64*a(n-3) for n >= 3.
a(n) = 12*a(n-1) - 32*a(n-2) + 2^n with a(0)=1, a(1)=14. (End)
MAPLE
seq((2^n-6*4^n+8*8^n)/3, n=0..20);
seq(binomial(2^n, 3)/4, n=2..20); # Zerinvary Lajos, Feb 22 2008
MATHEMATICA
CoefficientList[Series[1/((1-2x)(1-4x)(1-8x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{14, -56, 64}, {1, 14, 140}, 30] (* Harvey P. Dale, Jul 23 2011 *)
PROG
(Magma) [(2^n-6*4^n+8*8^n)/3 : n in [0..20]]; // Wesley Ivan Hurt, Jul 07 2014
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
STATUS
approved