OFFSET
1,2
COMMENTS
For every odd n the triple (a(n-1)^2, a(n)^2 , a(n+1)^2) is an arithmetic progression, i.e., 2*a(n)^2 = a(n-1)^2 + a(n+1)^2.
In general a triple((x-y)^2,z^2,(x+y)^2) is an arithmetic progression if and only if x^2+y^2=z^2.
The first differences of this sequence is the interleaved sequence 28,12,44,28,60,44....
FORMULA
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4).
O.G.f.: (1+27*x-17*x^2+5*x^3)/((1+x)*(1-x)^3).
a(n) = 4*n*(n+3)-6*(-1)^n+7.
2*a(2n+1)^2 = a(2n)^2 + a(2n+2)^2.
EXAMPLE
a(4) = 2*a(3) - 2*a(1) + a(0) = 2*85 - 2*29 + 1 = 113.
PROG
(Magma) I:=[1, 29, 41, 85]; [n le 4 select I[n] else 2*Self(n-1)-2*Self(n-3)+Self(n-4): n in [1..75]];
(Maxima) A214405(n):=4*n*(n+3)-6*(-1)^n+7$
makelist(A214405(n), n, 0, 30); /* Martin Ettl, Nov 01 2012 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Yasir Karamelghani Gasmallah, Jul 15 2012
STATUS
approved