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a(n) = (11^n - 1)/(5*2^(3 - 2*(n mod 2))).
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%I #16 Oct 21 2024 17:09:47

%S 0,1,3,133,366,16105,44289,1948717,5358972,235794769,648435615,

%T 28531167061,78460709418,3452271214393,9493745839581,417724816941565,

%U 1148743246589304,50544702849929377,138997932837305787,6115909044841454629,16818749873314000230,740024994425816010121,2035068734670994027833

%N a(n) = (11^n - 1)/(5*2^(3 - 2*(n mod 2))).

%C There are simple linear recurrences for this sequence and several related ones. The general signature is (0, p^2+1, 0, -p^2), where p is the prime in the numerator of the formula (here p = 11). The recurrence can be verified by substituting the definition in the recurrence (cf. the "simplify" statement in the Maple code, below). - _Georg Fischer_, Oct 20 2024

%H Ray Chandler, <a href="/A152435/b152435.txt">Table of n, a(n) for n = 0..961</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 122, 0, -121)

%F a(n) = -121*a(n-4) + 122*a(n-2). - _Georg Fischer_, Oct 19 2024

%p a := proc(n): (11^n - 1)/(5*2^(3 - 2*(n mod 2))): end: seq(a(n), n=0..22);

%p simplify(-121*a(n-4)+122*a(n-2)-a(n)) = 0; # _Georg Fischer_, Oct 19 2024

%t a[n_] := (11^n - 1)/(5*2^(3 - 2*Mod[n, 2]));

%t Table[a[n], {n, 0, 30}]

%Y Cf. A152298 (p=3), A152417 (p=5), A152418 (p=7), this sequence (p=11), A152436 (p=13), A152437 (p=17), A152438 (p=19).

%K nonn,easy

%O 0,3

%A _Roger L. Bagula_, Dec 04 2008