A096978 Sum of the areas of the first n Jacobsthal rectangles.

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (4,3,-14,8).

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

Cf. A096977, A064831.

Sequence in context: A110688 A218920 A009450 * A186810 A167478 A094734

Adjacent sequences: A096975 A096976 A096977 * A096979 A096980 A096981

Keyword

easy,nonn

Author

Paul Barry, Jul 17 2004

Status

approved