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

Author

Paul Barry, Mar 23 2003

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A016921, A081580, A081590.

Programs

Magma

[1-6*n+18*n^2: n in [0..40]]; // Vincenzo Librandi, Aug 09 2013

Mathematica

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

PARI

a(n)=18*n^2-6*n+1 \\ Charles R Greathouse IV, Jun 17 2017

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)