A081275 Shallow diagonal of triangular spiral in A051682.

1, 31, 97, 199, 337, 511, 721, 967, 1249, 1567, 1921, 2311, 2737, 3199, 3697, 4231, 4801, 5407, 6049, 6727, 7441, 8191, 8977, 9799, 10657, 11551, 12481, 13447, 14449, 15487, 16561, 17671, 18817, 19999, 21217, 22471, 23761, 25087, 26449, 27847, 29281, 30751, 32257

Offset: 0

Author

Paul Barry, Mar 15 2003

Keywords

• nonn
• easy

Comments

Reflection of A060544 in the horizontal A051682.

Binomial transform of (1, 30, 36, 0, 0, 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).

Crossrefs

Cf. A051682, A060544, A092296.

Programs

Mathematica

Table[30Binomial[n,1]+36Binomial[n,2]+1,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{1,31,97},40] (* Harvey P. Dale, Jun 30 2011 *)
CoefficientList[Series[(1 + 28 x + 7 x^2) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 07 2013 *)

PARI

a(n)=18*n^2+12*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = C(n,0) + 30*C(n,1) + 36*C(n,2).

a(n) = 18*n^2 + 12*n + 1.

G.f.: (1 + 28*x + 7*x^2)/(1-x)^3.

a(0)=1, a(1)=31, a(2)=97, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jun 30 2011

E.g.f.: exp(x)*(1 + 30*x + 18*x^2). - Elmo R. Oliveira, Nov 13 2024