OFFSET
0,2
COMMENTS
Diagonal sums of number triangle A106246. Transform of C(2,n)=(1,2,1,0,0,0,...) under the mapping that takes g(x) to (1/(1-x^2))g(x/(1-x^2)).
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).
FORMULA
From Colin Barker, Jul 23 2016: (Start)
a(n) = (16+10*n+(-1)^n*(-6+n)*n+n^2)/16.
a(n) = (n^2+2*n+8)/8 for n even.
a(n) = n+1 for n odd.
a(n) = 3*a(n-2)-3*a(n-4)+a(n-6) for n>5.
(End)
MATHEMATICA
CoefficientList[Series[(1+2x-x^2-2x^3+x^4)/(1-x^2)^3, {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 3, 0, -3, 0, 1}, {1, 2, 2, 4, 4, 6}, 100] (* Harvey P. Dale, Mar 23 2023 *)
PROG
(PARI) Vec((1+2*x-x^2-2*x^3+x^4)/(1-x^2)^3 + O(x^100)) \\ Colin Barker, Jul 23 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 26 2005
STATUS
approved