OFFSET
1,3
COMMENTS
(1) a(2n) = n^2, a(2n-1) = n(n+1) = twice the n-th triangular number. (2) Geometric mean of the successive squares interleaved between them.
Essentially the same as A002620.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
FORMULA
a(n+1) + a(n) = binomial(n+1,2), a(1) = a(2) = 1. - G. C. Greubel, Oct 29 2017
From Stefano Spezia, Nov 16 2024: (Start)
a(n) = (2*n^2 - (-1)^n - 1)/8 for n > 1.
G.f.: x*(1 - x + 2*x^2 - x^4)/((1 - x)^3*(1 + x)).
E.g.f.: (4*x + x*(1 + x)*cosh(x) - (1 - x - x^2)*sinh(x))/4. (End)
MATHEMATICA
Join[{1}, LinearRecurrence[{2, 0, -2, 1}, {1, 2, 4, 6}, 50]] (* G. C. Greubel, Oct 29 2017 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Amarnath Murthy, Oct 17 2002
EXTENSIONS
More terms from Philippe Deléham, Jun 20 2005
STATUS
approved