A247817 - OEIS

%I #22 Feb 19 2023 14:59:16

%S 0,16,80,336,1360,5456,21840,87376,349520,1398096,5592400,22369616,

%T 89478480,357913936,1431655760,5726623056,22906492240,91625968976,

%U 366503875920,1466015503696,5864062014800,23456248059216,93824992236880,375299968947536,1501199875790160

%N Sum(4^k, k=2..n).

%H Vincenzo Librandi, <a href="/A247817/b247817.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).

%F G.f.: 16*x^2/((1-x)*(1-4*x)).

%F a(n) = a(n-1) + 4^n = (4^(n+1) - 16)/3 = 5*a(n-1) - 4*a(n-2).

%F a(n) = A080674(n) - 4. - _Michel Marcus_, Sep 25 2014

%t RecurrenceTable[{a[1] == 0, a[n] == a[n-1] + 4^n}, a, {n, 30}] (* or *) CoefficientList[ Series[16 x / ((1 - x) (1 - 4 x)),{x, 0, 40}], x]

%t LinearRecurrence[{5,-4},{0,16},30] (* _Harvey P. Dale_, Feb 19 2023 *)

%o (Magma) [0] cat [&+[4^k: k in [2..n]]: n in [2..30]]; /* or */ [(4^(n+1)-16)/3: n in [1..30]];

%o (PARI) a(n) = sum(k=2, n, 4^k); \\ _Michel Marcus_, Sep 25 2014

%Y Cf. Sum(h^k,k=2..n): A028329 (h=2), A168569 (h=3), this sequence (h=4), A168571 (h=5), A247840 (h=6), A168572 (h=7), A247841 (h=8), A247842 (h=9), A124166 (h=10).

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Sep 25 2014