A152435 a(n) = (11^n - 1)/(5*2^(3 - 2*(n mod 2))).

0, 1, 3, 133, 366, 16105, 44289, 1948717, 5358972, 235794769, 648435615, 28531167061, 78460709418, 3452271214393, 9493745839581, 417724816941565, 1148743246589304, 50544702849929377, 138997932837305787, 6115909044841454629, 16818749873314000230, 740024994425816010121, 2035068734670994027833

Offset

0,3

Comments

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

Links

Ray Chandler, Table of n, a(n) for n = 0..961

Index entries for linear recurrences with constant coefficients, signature (0, 122, 0, -121)

Formula

a(n) = -121*a(n-4) + 122*a(n-2). - Georg Fischer, Oct 19 2024

Maple

a := proc(n): (11^n - 1)/(5*2^(3 - 2*(n mod 2))): end: seq(a(n), n=0..22);
simplify(-121*a(n-4)+122*a(n-2)-a(n)) = 0; # Georg Fischer, Oct 19 2024

Mathematica

a[n_] := (11^n - 1)/(5*2^(3 - 2*Mod[n, 2]));
Table[a[n], {n, 0, 30}]

Crossrefs

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

Sequence in context: A048796 A213203 A199141 * A239426 A157086 A366306

Adjacent sequences: A152432 A152433 A152434 * A152436 A152437 A152438

Keyword

nonn,easy

Author

Roger L. Bagula, Dec 04 2008

Status

approved