OFFSET
0,2
COMMENTS
It appears that a(2*n+1) = 2*(n + A002623(2*n-1)) + 3. - Carl Najafi, Jan 21 2013
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
FORMULA
a(n) = (1/24)*(4*n^3 + 12*n^2 + 20*n + 33 + (6*n^2 - 9)*(-1)^n). - Ralf Stephan, Dec 02 2004
G.f.: (1 + 2*x + x^2 - 2*x^3 + 7*x^4 - x^6)/((1 + x)^3*(x - 1)^4). - R. J. Mathar, May 20 2013
E.g.f.: ((12 + 15*x + 15*x^2 + 2*x^3)*cosh(x) + (21 + 21*x + 9*x^2 + 2*x^3)*sinh(x))/12. - Stefano Spezia, Apr 18 2023
EXAMPLE
a(0) = 1
a(1) = 1+2
a(2) = 1+2*3
a(3) = 1+2*3+4
a(4) = 1+2*3+4*5
a(5) = 1+2*3+4*5+6
a(6) = 1+2*3+4*5+6*7
a(7) = 1+2*3+4*5+6*7+8
a(8) = 1+2*3+4*5+6*7+8*9
MATHEMATICA
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 3, 7, 11, 27, 33, 69}, 50] (* Harvey P. Dale, Jun 02 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jorge Coveiro, Apr 28 2004
EXTENSIONS
More terms from Ralf Stephan, Dec 02 2004
STATUS
approved