A257548 a(1) = 1, a(2) = 2, a(3) = 5, a(4) = 8 and a(5) = 15, a(n) = Sum_{j=1..n-1} a(j).

1, 2, 5, 8, 15, 31, 62, 124, 248, 496, 992, 1984, 3968, 7936, 15872, 31744, 63488, 126976, 253952, 507904, 1015808, 2031616, 4063232, 8126464, 16252928, 32505856, 65011712, 130023424, 260046848, 520093696, 1040187392, 2080374784, 4160749568, 8321499136

Offset

1,2

Comments

31 is the only prime after 5 (the remaining terms are even).

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2).

Formula

For n>=6, a(n) = 31*2^(n-6).

For n>=6, a(n) = A206371(n-6) - 1.

G.f.: x*(1+x^2-2*x^3-x^4+x^5)/(1-2*x). - Robert G. Wilson v, May 05 2015

E.g.f.: (31/64)*exp(2*x) + x/32 + x^2/32 + 3*x^3/16 + x^4/96 - x^5/240. - G. C. Greubel, Jan 05 2023

Mathematica

Join[{1, 2, 5, 8, 15}, Table[31*2^(n-6), {n, 6, 50}]] (* Vincenzo Librandi, May 03 2015 *)
CoefficientList[ Series[(x^5 -x^4 -2x^3 +x^2 +1)/(1 -2x), {x, 0, 33}], x] (* Robert G. Wilson v, May 05 2015 *)
Join[{1, 2, 5, 8, 15}, NestList[2#&, 31, 30]] (* Harvey P. Dale, Oct 09 2018 *)

Prog

(Magma) [1, 2, 5, 8] cat [31*2^n div 64: n in [5..50]]; // Vincenzo Librandi, May 03 2015
(SageMath)
def A257548(n): return (4*fibonacci(n+1) -3 -(-1)^n)/2 if (n<6) else 31*2^(n-6)
[A257548(n) for n in range(1, 51)] # G. C. Greubel, Jan 05 2023

Crossrefs

Cf. A206371.

Sequence in context: A081660 A285291 A065618 * A186413 A080084 A065093

Adjacent sequences: A257545 A257546 A257547 * A257549 A257550 A257551

Keyword

nonn,easy

Author

Giovanni Teofilatto, Apr 29 2015

Status

approved