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
Examples
If n=3 then a(3) = 34*a(2) - a(1) + 2 = 545 which is the third term in the sequence.
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).
Programs
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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 *) -
PARI
Vec(x*(1-19*x+20*x^2)/((1-x)*(1-34*x+x^2)) + O(x^20)) \\ Colin Barker, Mar 02 2016
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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
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
Extensions
Definition corrected by Rick L. Shepherd, Aug 17 2007
More terms from Harvey P. Dale, Feb 10 2015