A081589 Third row of Pascal-(1,5,1) array A081580.

1, 13, 61, 145, 265, 421, 613, 841, 1105, 1405, 1741, 2113, 2521, 2965, 3445, 3961, 4513, 5101, 5725, 6385, 7081, 7813, 8581, 9385, 10225, 11101, 12013, 12961, 13945, 14965, 16021, 17113, 18241, 19405, 20605, 21841, 23113, 24421, 25765, 27145, 28561, 30013, 31501

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 - 6*n + 18*n^2.

G.f.: (1+5*x)^2/(1-x)^3.

From Elmo R. Oliveira, Jun 06 2025: (Start)

E.g.f.: exp(x)*(1 + 12*x + 18*x^2).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

Mathematica

CoefficientList[Series[(1 + 5 x)^2 / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 09 2013 *)

Prog

(Magma) [1-6*n+18*n^2: n in [0..40]]; // Vincenzo Librandi, Aug 09 2013
(PARI) a(n)=18*n^2-6*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A016921, A081580, A081590.

Sequence in context: A140615 A086361 A119151 * A270449 A139880 A379896

Adjacent sequences: A081586 A081587 A081588 * A081590 A081591 A081592

Keyword

easy,nonn

Author

Paul Barry, Mar 23 2003

Status

approved