OFFSET
2,4
COMMENTS
For n>2, a(n)+a(n+1) seems to be A002620(n+1)+1.
LINKS
Colin Barker, Table of n, a(n) for n = 2..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
G.f.: x^2*(1 -2*x^2 +x^3 +2*x^4 -x^5)/((1-x)^3*(1+x)^2).
a(n) = A114220(n-1), n>=3. - R. J. Mathar, Feb 03 2013
From Colin Barker, Jan 27 2016: (Start)
a(n) = (2*n^2 +2*(-1)^n*n -6*n -11*(-1)^n +11)/16 for n>2.
a(n) = (n^2 - 2*n)/8 for n>2 and even.
a(n) = (n^2 - 4*n + 11)/8 for n odd. (End)
E.g.f.: (4*x*(x-2) + x*(x-3)*cosh(x) + (x^2 -x +11)*sinh(x))/8. - G. C. Greubel, Jan 23 2020
MAPLE
seq( `if`(n==2, 1, (2*n^2 -6*n +11 +(-1)^n*(2*n -11))/16), n=2..65); # G. C. Greubel, Jan 23 2020
MATHEMATICA
CoefficientList[Series[(1 -2*x^2 +x^3 +2*x^4 -x^5)/((1-x)^3*(1+x)^2), {x, 0, 65}], x] (* Wesley Ivan Hurt, Jan 20 2017 *)
Table[If[n==2, 1, (2*n^2 -6*n +11 +(-1)^n*(2*n -11))/16], {n, 2, 65}] (* G. C. Greubel, Jan 23 2020 *)
PROG
(PARI) Vec(x^2*(1-2*x^2+x^3+2*x^4-x^5)/((1-x)^3*(1+x)^2) + O(x^65)) \\ Charles R Greathouse IV, Feb 03 2013
(PARI) vector(65, n, my(m=n+1); if(m==2, 1, (2*m^2 -6*m +11 +(-1)^m*(2*m -11))/16)) \\ G. C. Greubel, Jan 23 2020
(Magma) [1] cat [(2*n^2 -6*n +11 +(-1)^n*(2*n -11))/16: n in [3..65]]; // G. C. Greubel, Jan 23 2020
(Sage) [1]+[(2*n^2 -6*n +11 +(-1)^n*(2*n -11))/16 for n in (3..65)] # G. C. Greubel, Jan 23 2020
(GAP) Concatenation([1], List([3..65], n-> (2*n^2 -6*n +11 +(-1)^n*(2*n -11))/16 )); # G. C. Greubel, Jan 23 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 28 2000
STATUS
approved