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A131515
a(n+2) = 34*a(n+1) - a(n) + 2; a(1) = 1 and a(2) = 16.
1
1, 16, 545, 18516, 629001, 21367520, 725866681, 24658099636, 837649520945, 28455425612496, 966646821303921, 32837536498720820, 1115509594135203961, 37894488664098213856, 1287297104985204067145, 43730207080832840069076, 1485539743643331358281441
OFFSET
1,2
LINKS
Chip Curtis, Generating Heronian Triangles, The College Mathematics Journal, vol. 38 (2007), pp. 315-316. See page 316.
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
Sequence in context: A187160 A196216 A196683 * A223106 A268564 A268566
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