A332243 Starhex honeycomb numbers: a(n) = 13 + 60*n + 60*n^2.

13, 133, 373, 733, 1213, 1813, 2533, 3373, 4333, 5413, 6613, 7933, 9373, 10933, 12613, 14413, 16333, 18373, 20533, 22813, 25213, 27733, 30373, 33133, 36013, 39013, 42133, 45373, 48733, 52213, 55813, 59533, 63373, 67333, 71413, 75613, 79933, 84373

Offset

0,1

References

M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 20.

Links

Table of n, a(n) for n=0..37.

John Elias, Illustration of Initial Terms

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

Formula

a(n) = 12*(5*n*(n + 1) + 1) + 1.

From Stefano Spezia, Feb 07 2020: (Start)

O.g.f.: (13 + 94*x + 13*x^2)/(1 - x)^3.

E.g.f.: exp(x)*(13 + 120*x + 60*x^2).

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

a(n) = A082369(A001844(n)). - M. F. Hasler, Jun 09 2023

Example

Example: a(2) = 13 + 60*2 + 60*2^2 = 373.
Illustration of initial terms:
.                               0
.                            0 0 0 0
.                             0 0 0
.                      0     0 0 0 0     0
.                   0 0 0 0 * * 0 * * 0 0 0 0
.                    0 0 0 * * * * * * 0 0 0
.                   0 0 0 0 * * 0 * * 0 0 0 0
.                      0 * * 0 0 0 0 * * 0
.                       * * * 0 0 0 * * *
.                      0 * * 0 0 0 0 * * 0
.                   0 0 0 0 * * 0 * * 0 0 0 0
.                    0 0 0 * * * * * * 0 0 0
.    0              0 0 0 0 * * 0 * * 0 0 0 0
. 0 * * 0              0     0 0 0 0     0
.  * 0 *                      0 0 0
. 0 * * 0                    0 0 0 0
.    0                          0
.
.    13                         133

Mathematica

Array[12 (5 #^2 + 5 # + 1) + 1 &, 38, 0] (* Michael De Vlieger, Feb 07 2020 *)
LinearRecurrence[{3, -3, 1}, {13, 133, 373}, 40] (* Harvey P. Dale, Nov 18 2023 *)

Prog

(PARI) A332243(n)=n*(n+1)*60+13 \\ M. F. Hasler, Jun 09 2023

Crossrefs

Cf. A003154, A003215, A062786.

Subsequence of A082369: cf. formula.

Sequence in context: A295603 A199144 A198664 * A081042 A329019 A016153

Adjacent sequences: A332240 A332241 A332242 * A332244 A332245 A332246

Keyword

easy,nonn

Author

John Elias, Feb 07 2020

Status

approved