A278708 Fibonacci sequence starting 154, 144.

154, 144, 298, 442, 740, 1182, 1922, 3104, 5026, 8130, 13156, 21286, 34442, 55728, 90170, 145898, 236068, 381966, 618034, 1000000, 1618034, 2618034, 4236068, 6854102, 11090170, 17944272, 29034442, 46978714, 76013156, 122991870, 199005026, 321996896, 521001922

Offset

1,1

Comments

The number 1000000 is in this sequence. There is a famous problem that says that somebody deposited money into a bank 20 times, and each deposit was the sum of the previous two deposits. The final deposit was $1000000. What were the first two deposits? The answer is $154 and $144, leading to this sequence.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..4776

Perplexus Dot Info contributor Ady Tzidon, Twenty deposits.

Index entries for linear recurrences with constant coefficients, signature (1,1).

Formula

From Elmo R. Oliveira, Mar 31 2026: (Start)

G.f.: -2*(82*x-5)/(x^2+x-1).

a(n) = a(n-1) + a(n-2) for n > 2.

a(n) = 154*Fibonacci(n) - 10*Fibonacci(n-1). (End)

Maple

a:= n-> (<<0|1>, <1|1>>^n.<<-10, 154>>)[1, 1]:
seq(a(n), n=1..33);  # Alois P. Heinz, Mar 31 2026

Mathematica

LinearRecurrence[{1, 1}, {154, 144}, 33] (* Michael De Vlieger, Oct 03 2023 *)

Crossrefs

Cf. A000045.

Sequence in context: A269664 A384357 A281857 * A206266 A049515 A049519

Adjacent sequences: A278705 A278706 A278707 * A278709 A278710 A278711

Keyword

nonn,easy

Author

Bobby Jacobs, Jan 11 2017

Extensions

More terms from Rémy Sigrist, Oct 03 2023

Status

approved