A081593 Third row of Pascal-(1,7,1) array A081582.
1, 17, 97, 241, 449, 721, 1057, 1457, 1921, 2449, 3041, 3697, 4417, 5201, 6049, 6961, 7937, 8977, 10081, 11249, 12481, 13777, 15137, 16561, 18049, 19601, 21217, 22897, 24641, 26449, 28321, 30257, 32257, 34321, 36449, 38641, 40897, 43217, 45601, 48049, 50561, 53137
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[1-16*n+32*n^2: n in [0..40]]; // Vincenzo Librandi, Aug 09 2013
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Mathematica
CoefficientList[Series[(1 + 7 x)^2 / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 09 2013 *) LinearRecurrence[{3,-3,1},{1,17,97},50] (* Harvey P. Dale, Aug 30 2025 *) -
PARI
a(n)=32*n^2-16*n+1 \\ Charles R Greathouse IV, Jun 17 2017
Formula
a(n) = 1 - 16*n + 32*n^2.
G.f.: (1+7*x)^2/(1-x)^3.
From Elmo R. Oliveira, Jun 09 2025: (Start)
E.g.f.: exp(x)*(1 + 16*x + 32*x^2).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)