A014928 a(1)=1, a(n) = n*13^(n-1) + a(n-1).

1, 27, 534, 9322, 152127, 2379885, 36167548, 538155684, 7879732173, 113924725903, 1630368136242, 23136292864686, 326011399456939, 4566262891748481, 63626908677237816, 882601196902689928, 12194683553016747225, 167902170101880830019, 2304554902189071299470

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..900

Index entries for linear recurrences with constant coefficients, signature (27,-195,169).

Formula

From Vincenzo Librandi, Oct 23 2012: (Start)

a(n) = 26*a(n-1) - 169*a(n-2) + 1, a(1)=1, a(2)=27.

G.f.: x/((1-x)*(1-13*x)^2). (End)

a(n) = 27*a(n-1) - 195*a(n-2) + 169*a(n-3), a(1)=1, a(2)=27, a(3)=534. - Harvey P. Dale, Jan 20 2015

From Elmo R. Oliveira, May 16 2025: (Start)

E.g.f.: exp(x)*(1 + exp(12*x)*(156*x - 1))/144.

a(n) = (13^n*(12*n - 1) + 1)/144. (End)

Mathematica

CoefficientList[Series[1/((1 - x)(1 - 13*x)^2), {x, 0, 900}], x] (* Vincenzo Librandi, Oct 23 2012 *)
RecurrenceTable[{a[1]==1, a[n]==n*13^(n-1)+a[n-1]}, a, {n, 20}] (* or *) LinearRecurrence[{27, -195, 169}, {1, 27, 534}, 20] (* Harvey P. Dale, Jan 20 2015 *)

Prog

(Magma) I:=[1, 27]; [n le 2 select I[n] else 26*Self(n-1)-169*Self(n-2)+1: n in [1..20]]; // Vincenzo Librandi, Oct 23 2012

Crossrefs

Sequence in context: A016887 A110896 A215039 * A163199 A051561 A163197

Adjacent sequences: A014925 A014926 A014927 * A014929 A014930 A014931

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved