A072818 Expansion of g.f. 20*x/(1-98*x+x^2).

0, 20, 1960, 192060, 18819920, 1844160100, 180708869880, 17707625088140, 1735166549767840, 170028614252160180, 16661069030161929800, 1632614736341616960220, 159979583092448300171760, 15676366528323591799872260, 1536123940192619548087309720, 150524469772348392120756480300

Offset

0,2

Comments

Previous name was: Possibly the only integers of the form sqrt(m^2*(m^2-1)*2/3) [only checked for the first 5 terms].

These are the standard deviations of time for a random walk starting at 0 to reach one of the boundaries at +A001079(n) or -A001079(n) for the first time.

Links

Indranil Ghosh, Table of n, a(n) for n = 0..501

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (98,-1).

Formula

a(n) = 98*a(n-1)-a(n-2) for n > 1.

a(n) = sqrt(A072819(A001079(n))).

G.f.: 20*x/(1-98*x+x^2). - Philippe Deléham, Nov 18 2008

E.g.f.: exp(49*x)*sinh(20*sqrt(6)*x)/sqrt(6). - Stefano Spezia, May 31 2026

a(n) = 20 * A173205(n). - Alois P. Heinz, May 31 2026

Example

0 and 20 are at the start of the sequence since m^2*(m^2-1)*2/3 (A072819) starts 0, 0, 8, 48, 160, 400, 840, 1568, ... and the only squares among these are 0 and 400 with square roots of 0 and 20.

Prog

(PARI) a(n)=([0, 1; -1, 98]^n*[0; 20])[1, 1] \\ Charles R Greathouse IV, May 29 2026

Crossrefs

Cf. A072819, A001079, A173205.

Sequence in context: A246619 A222973 A267575 * A123479 A071152 A195622

Adjacent sequences: A072815 A072816 A072817 * A072819 A072820 A072821

Keyword

nonn,easy,changed

Author

Henry Bottomley, Jul 14 2002

Extensions

New name using g.f. by Philippe Deléham from Joerg Arndt, May 31 2026

Status

approved