A014930 a(1)=1, a(n) = n*15^(n-1) + a(n-1).

1, 31, 706, 14206, 267331, 4823581, 84557956, 1451432956, 24517448581, 408951042331, 6752105339206, 110549175651706, 1797251568229831, 29043982525261081, 466937872906120456, 7473240118999870456, 119136182166119011081, 1892606438208599479831, 29972552158881206901706

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Index entries for linear recurrences with constant coefficients, signature (31,-255,225).

Formula

G.f.: x/((1 - x)*(1 - 15*x)^2). - Stefano Spezia, Mar 11 2020

From Elmo R. Oliveira, May 21 2025: (Start)

E.g.f.: exp(x)*(1 + exp(14*x)*(210*x - 1))/196.

a(n) = (15^n*(14*n - 1) + 1)/196.

a(n) = 30*a(n-1) - 225*a(n-2) + 1 for n > 2.

a(n) = 31*a(n-1) - 255*a(n-2) + 225*a(n-3) for n >= 4. (End)

Prog

(PARI) a(n) = (1+15^n*(14*n-1))/196; \\ Jinyuan Wang, Mar 11 2020
(PARI) Vec(-x/((x-1)*(15*x-1)^2) + O(x^20)) \\ Elmo R. Oliveira, May 21 2025

Crossrefs

Sequence in context: A362512 A006097 A000565 * A196988 A358179 A061252

Adjacent sequences: A014927 A014928 A014929 * A014931 A014932 A014933

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

More terms from Elmo R. Oliveira, May 21 2025

Status

approved