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

0,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A051682, A060544, A092296.

Sequence in context: A159014 A256323 A142067 * A139509 A187517 A039463

Adjacent sequences: A081272 A081273 A081274 * A081276 A081277 A081278

Keyword

nonn,easy

Author

Paul Barry, Mar 15 2003

Status

approved