OFFSET
1,2
COMMENTS
Equals row sums of triangle A144336. - Gary W. Adamson, Sep 18 2008
REFERENCES
F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
F. Faase, Results from the counting program
Eric Weisstein's World of Mathematics, Hamiltonian Path
Eric Weisstein's World of Mathematics, Ladder Graph
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
For n>1, a(n) = n^2 - n + 2 = A014206(n-1).
Equals binomial transform of [1, 3, 1, 1, -1, 1, -1, 1, ...]. - Gary W. Adamson, Apr 23 2008
G.f.: x(1 + x - x^2 + x^3)/(1-x)^3. - R. J. Mathar, Dec 16 2008
a(n) = floor((n^3 + 2*n)/(n+1)). - Gary Detlefs, Feb 20 2010
Except for the first term, a(n) = 2*n + a(n-1), (with a(1)=4). - Vincenzo Librandi, Dec 06 2010
a(0)=1, a(1)=4, a(2)=8, a(3)=14, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jun 14 2011
Sum_{n>=1} 1/a(n) = 1/2 + Pi*tanh(Pi*sqrt(7)/2)/sqrt(7) = 1.686827... - R. J. Mathar, Apr 24 2024
MAPLE
a:=n->sum(binomial(2, 2*j)+n, j=0..n): seq(a(n), n=0..46); # Zerinvary Lajos, Feb 22 2007
seq(floor((n^3+2*n)/(n+1)), n=1..47); # Gary Detlefs, Feb 20 2010
MATHEMATICA
Join[{1}, Table[n^2 - n + 2, {n, 2, 50}]] (* Harvey P. Dale, Jun 14 2011 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {4, 8, 14}, 50]] (* Harvey P. Dale, Jun 14 2011 *)
PROG
(PARI) a(n)=if(n>1, n^2-n+2, 1) \\ Charles R Greathouse IV, Jan 05 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved