A037701 Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 1,2,3,0.

1, 12, 123, 1230, 12301, 123012, 1230123, 12301230, 123012301, 1230123012, 12301230123, 123012301230, 1230123012301, 12301230123012, 123012301230123, 1230123012301230, 12301230123012301, 123012301230123012, 1230123012301230123, 12301230123012301230

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Index entries for linear recurrences with constant coefficients, signature (10,0,0,1,-10).

Formula

a(0)=1, a(1)=12, a(2)=123, a(3)=1230, a(4)=12301, a(n) = 10*a(n-1) + a(n-4) - 10*a(n-5). - Harvey P. Dale, Jun 07 2011

G.f.: x*(1+2*x+3*x^2) / ( (x-1)*(10*x-1)*(1+x)*(x^2+1) ). - R. J. Mathar, Aug 12 2013

Mathematica

Rest[RecurrenceTable[{a[0]==0, a[n]==10a[n-1]+Mod[n, 4]}, a[n], {n, 20}]] (* or *) LinearRecurrence[{10, 0, 0, 1, -10}, {1, 12, 123, 1230, 12301}, 20] (* Harvey P. Dale, Jun 07 2011 *)

Prog

(PARI) Vec(x*(1+2*x+3*x^2)/((x-1)*(10*x-1)*(1+x)*(x^2+1)) + O(x^25)) \\ Jinyuan Wang, Apr 14 2020

Crossrefs

Sequence in context: A079847 A144165 A113572 * A037610 A035239 A344183

Adjacent sequences: A037698 A037699 A037700 * A037702 A037703 A037704

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

More terms from Harvey P. Dale, Jun 07 2011

Status

approved