A131515 a(n+2) = 34*a(n+1) - a(n) + 2; a(1) = 1 and a(2) = 16.

1, 16, 545, 18516, 629001, 21367520, 725866681, 24658099636, 837649520945, 28455425612496, 966646821303921, 32837536498720820, 1115509594135203961, 37894488664098213856, 1287297104985204067145, 43730207080832840069076, 1485539743643331358281441

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..650

Chip Curtis, Generating Heronian Triangles, The College Mathematics Journal, vol. 38 (2007), pp. 315-316. See page 316.

Index entries for linear recurrences with constant coefficients, signature (35,-35,1).

Formula

G.f.: -x*(1-19*x+20*x^2)/(-1+x)/(1-34*x+x^2). - R. J. Mathar, Nov 14 2007

a(1)=1, a(2)=16, a(3)=545, a(n) = 35*a(n-1)-35*a(n-2)+a(n-3). - Harvey P. Dale, Feb 10 2015

a(n) = (-6 + (963-680*sqrt(2))*(17+12*sqrt(2))^n + (17+12*sqrt(2))^(-n)*(963+680*sqrt(2)))/96. - Colin Barker, Mar 02 2016

Example

If n=3 then a(3) = 34*a(2) - a(1) + 2 = 545 which is the third term in the sequence.

Mathematica

RecurrenceTable[{a[1]==1, a[2]==16, a[n]==34a[n-1]-a[n-2]+2}, a, {n, 20}] (* or *) LinearRecurrence[{35, -35, 1}, {1, 16, 545}, 20] (* Harvey P. Dale, Feb 10 2015 *)

Prog

(PARI) Vec(x*(1-19*x+20*x^2)/((1-x)*(1-34*x+x^2)) + O(x^20)) \\ Colin Barker, Mar 02 2016
(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, -35, 35]^n*[20; 1; 16])[1, 1] \\ Charles R Greathouse IV, Aug 05 2016

Crossrefs

Cf. A016064, A001110.

Sequence in context: A187160 A196216 A196683 * A223106 A268564 A268566

Adjacent sequences: A131512 A131513 A131514 * A131516 A131517 A131518

Keyword

nonn,easy

Author

Parthasarathy Nambi, Aug 14 2007

Extensions

Definition corrected by Rick L. Shepherd, Aug 17 2007

More terms from Harvey P. Dale, Feb 10 2015

Status

approved