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A096978
Sum of the areas of the first n Jacobsthal rectangles.
2
0, 1, 4, 19, 74, 305, 1208, 4863, 19398, 77709, 310612, 1242907, 4970722, 19884713, 79535216, 318148151, 1272578046, 5090341317, 20361307020, 81445344595, 325781145370, 1303125047521, 5212499258024, 20849998896239, 83399991856694
OFFSET
0,3
FORMULA
G.f.: x/((1-x)^2*(1+2*x)*(1-4*x)).
a(n) = 8*4^n/27 - 2*(-2)^n/27 - (n+2)/9;
a(n) = Sum_{k=0..n} (2*4^k/3 + (-2)^k/3)*(n-k).
a(n) = 4*a(n-1) + 3*a(n-2) - 14*a(n-3) + 8*a(n-4).
a(n) = Sum_{k=0..n} A001045(k)*A001045(k+1).
a(n-1) = Sum_{k=0..n} (-1)^(k+1)*A001045(k)*A001045(2*(n-k)). - Paul Barry, Aug 11 2009
MATHEMATICA
LinearRecurrence[{4, 3, -14, 8}, {0, 1, 4, 19}, 30] (* or *) Table[(2^(2n+1)-3n - 3+(-2)^n)/27, {n, 30}] (* Harvey P. Dale, Aug 08 2011 *)
PROG
(Magma) [8*4^n/27-2*(-2)^n/27-(n+2)/9: n in [0..30]]; // Vincenzo Librandi, May 31 2011
CROSSREFS
Sequence in context: A110688 A218920 A009450 * A186810 A167478 A094734
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 17 2004
STATUS
approved