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A172416
a(n) = 5*2^n/9 + 1/4 + (-1)^n*(n/6 + 7/36).
2
1, 1, 3, 4, 10, 17, 37, 70, 144, 283, 571, 1136, 2278, 4549, 9105, 18202, 36412, 72815, 145639, 291268, 582546, 1165081, 2330173, 4660334, 9320680, 18641347, 37282707, 74565400, 149130814, 298261613, 596523241
OFFSET
0,3
COMMENTS
The sequence and the 1st, 2nd, 3rd etc. difference form the array
1, 1, 3, 4, 10, 17, 37, 70, 144, 283, 571, 1136,..
0, 2, 1, 6, 7, 20, 33, 74, 139, 288, 565, 1142, 2271,..
2, -1, 5, 1, 13, 13, 41, 65, 149, 277, 577, 1129, 2285,..
-3, 6, -4, 12, 0, 28, 24, 84, 128, 300, 552, 1156,...
where the sequence 1,2,5,12,.... = A045623 appears on the diagonal.
FORMULA
a(n) = a(n-1) + 3*a(n-2) - a(n-3) - 2*a(n-4).
a(n+1) - a(n) = A172285(n).
a(2n) = A164044(n).
a(2n+1) = A172447(n).
a(n+1) - 2*a(n) = (-1)^(n+1)*A008619(n).
G.f.: ( 1 - x^2 - x^3 ) / ( (2*x-1)*(x-1)*(1+x)^2 ).
PROG
(Magma) [5*2^n/9 +1/4 +(-1)^n*(n/6+7/36): n in [0..40]]; // Vincenzo Librandi, Aug 05 2011
CROSSREFS
Sequence in context: A224073 A034774 A342536 * A317883 A337089 A144958
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Feb 02 2010
STATUS
approved