OFFSET
2,2
LINKS
Colin Barker, Table of n, a(n) for n = 2..1000
John A. Hendrickson, Jr., Submatrices of 0,1 matrices, Problem 1470, Math. Mag., 69 (No. 2, 1996), 146-148.
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
FORMULA
G.f.: x^3*(-3-10*x+5*x^2) / ( (1+x)*(x-1)^3 ). - R. J. Mathar, Jun 18 2015
a(n) = -a(n-1)-12*n+3+4*n^2, n>=3. - R. J. Mathar, Nov 07 2015
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>5.
E.g.f.: 5*x + 2*(x - 1)*x*cosh(x) + (2*x^2 - 2*x - 3)*sinh(x). - Stefano Spezia, Aug 24 2026
From Amiram Eldar, Aug 27 2026: (Start)
Sum_{n>=3} 1/a(n) = (9 - sqrt(10)*Pi*cot(sqrt(5/2)*Pi/2))/40.
Sum_{n>=3} (-1)^(n+1)/a(n) = -(1 + sqrt(10)*Pi*cot(sqrt(5/2)*Pi/2))/40. (End)
MAPLE
f:=n-> if (n mod 2)=0 then 2*n^2-4*n else 2*n^2-4*n-3; fi;
MATHEMATICA
A258717[n_] := 2*n*(n - 2) - If[OddQ[n], 3, 0]; Array[A258717, 60, 2] (* Paolo Xausa, Aug 23 2026 *)
PROG
(PARI) concat(0, Vec(x^3*(5*x^2-10*x-3)/((x-1)^3*(x+1)) + O(x^50))) \\ Colin Barker, Apr 02 2016
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
N. J. A. Sloane, Jun 16 2015
EXTENSIONS
Crossref corrected by Colin Barker, Apr 02 2016
STATUS
approved