A362438 a(n) = n^2 + 2^(n-1).

2, 6, 13, 24, 41, 68, 113, 192, 337, 612, 1145, 2192, 4265, 8388, 16609, 33024, 65825, 131396, 262505, 524688, 1049017, 2097636, 4194833, 8389184, 16777841, 33555108, 67109593, 134218512, 268436297, 536871812, 1073742785, 2147484672, 4294968385, 8589935748, 17179870409, 34359739664, 68719478105, 137438954916

Offset

1,1

References

GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See page 79.

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Formula

From Chai Wah Wu, Apr 23 2023: (Start)

a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n > 4.

G.f.: x*(-x^3 + x^2 - 4*x + 2)/((x - 1)^3*(2*x - 1)). (End)

Mathematica

Table[n^2 + 2^(n-1), {n, 50}] (* Paolo Xausa, Jul 20 2024 *)

Prog

(Python)
def A362438(n): return n**2+(1<<n-1) # Chai Wah Wu, Apr 23 2023

Crossrefs

See A001580 for another version.

Sequence in context: A178532 A003600 A283551 * A000135 A281865 A267698

Adjacent sequences: A362435 A362436 A362437 * A362439 A362440 A362441

Keyword

nonn

Author

N. J. A. Sloane, Apr 21 2023

Status

approved