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
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (2).
Crossrefs
Cf. A206371.
Programs
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Magma
[1,2,5,8] cat [31*2^n div 64: n in [5..50]]; // Vincenzo Librandi, May 03 2015
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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 *) -
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
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
Comments