OFFSET
1,2
COMMENTS
All terms are odd. Sequence is infinite. Corresponding m's are 0, 6, 88, 1230, 17136, 238678, 3324360, 46302366, 644908768, 8982420390, 125108976696, 1742543253358, 24270496570320. s^2 are squares in A056109.
The Diophantine equation A000290(x) = A000326(y) + A000326(y-1) has the solutions x = a(n) and y = (4^n + (1 + sqrt(3))^(4*n - 3) + (1 - sqrt(3))^(4*n - 3))/(3*2^(2*n - 1)). - Bruno Berselli, Mar 04 2013
LINKS
Tanya Khovanova, Recursive Sequences
Valcho Milchev and Tsvetelina Karamfilova, Domino tiling in grid - new dependence, arXiv:1707.09741 [math.HO], 2017.
Index entries for linear recurrences with constant coefficients, signature (14,-1).
FORMULA
Alternatively, with a different offset:
a(0) = 1, a(1) = 11, a(n) = 14*a(n-1) - a(n-2), and
a(n) = ((3 - b)*(7 - 4*b)^n + (3 + b)*(7 + 4*b)^n)/6, b = sqrt(3).
a(n) = -(1/6)*sqrt(3)*(7 - 4*sqrt(3))^n + (1/6)*sqrt(3)*(7 + 4*sqrt(3))^n + (1/2)*(7 + 4*sqrt(3))^n + (1/2)*(7 - 4*sqrt(3))^n. [Paolo P. Lava, Aug 06 2008]
G.f.: x*(1 - 3*x)/(1 - 14*x + x^2). [Philippe Deléham, Nov 17 2008]
E.g.f.: (1/3)*((9*cosh(4*sqrt(3)*x) - 5*sqrt(3)*sinh(4*sqrt(3)*x))*exp(7*x) - 9). - Franck Maminirina Ramaharo, Jan 07 2019
MATHEMATICA
LinearRecurrence[{14, -1}, {1, 11}, 17] (* Jean-François Alcover, Jan 07 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Oct 21 2006
EXTENSIONS
Edited by N. J. A. Sloane, Oct 28 2006
STATUS
editing