A081268 Diagonal of triangular spiral in A051682.

1, 12, 32, 61, 99, 146, 202, 267, 341, 424, 516, 617, 727, 846, 974, 1111, 1257, 1412, 1576, 1749, 1931, 2122, 2322, 2531, 2749, 2976, 3212, 3457, 3711, 3974, 4246, 4527, 4817, 5116, 5424, 5741, 6067, 6402, 6746, 7099, 7461, 7832, 8212, 8601, 8999, 9406

Offset: 0

Author

Paul Barry, Mar 15 2003

Keywords

• easy
• nonn

Examples

			a(1) = 9*1 +  1 + 2 = 12.
a(2) = 9*2 + 12 + 2 = 32.
a(3) = 9*3 + 32 + 2 = 61.
		

Links

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

Crossrefs

Cf. A064226, A081267.

Programs

PARI

a(n)=(9*n^2+13*n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = C(n,0) + 11*C(n,1) + 9*C(n,2); binomial transform of (1, 11, 9, 0, 0, 0, ...).

a(n) = (9*n^2 + 13*n + 2)/2.

G.f.: (1 + 9*x - x^2)/(1-x)^3.

a(n) = 9*n + a(n-1) + 2 (with a(0)=1). - Vincenzo Librandi, Aug 08 2010

From Elmo R. Oliveira, Nov 16 2024: (Start)

E.g.f.: exp(x)*(9*x^2 + 22*x + 2)/2.

a(n) = A064226(n) - 2.

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