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

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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)

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 *)

Prog

(Magma) [1-16*n+32*n^2: n in [0..40]]; // Vincenzo Librandi, Aug 09 2013
(PARI) a(n)=32*n^2-16*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A017077, A081582, A081594.

Sequence in context: A142189 A325068 A264823 * A078901 A078902 A103766

Adjacent sequences: A081590 A081591 A081592 * A081594 A081595 A081596

Keyword

easy,nonn

Author

Paul Barry, Mar 23 2003

Status

approved