

A242658


a(n) = 3n^23n+2.


3



2, 2, 8, 20, 38, 62, 92, 128, 170, 218, 272, 332, 398, 470, 548, 632, 722, 818, 920, 1028, 1142, 1262, 1388, 1520, 1658, 1802, 1952, 2108, 2270, 2438, 2612, 2792, 2978, 3170, 3368, 3572, 3782, 3998, 4220, 4448, 4682, 4922, 5168, 5420, 5678, 5942, 6212, 6488, 6770, 7058, 7352
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OFFSET

0,1


COMMENTS

An exercise in Smith (1950), my secondary school algebra book.
For n > 0, also the number of (not necessarily maximum) cliques in the (n1)triangular grid graph.  Eric W. Weisstein, Nov 29 2017


REFERENCES

C. Smith, A Treatise on Algebra, Macmillan, London, 5th ed., 1950, p. 429, Example 2(i).


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Clique
Eric Weisstein's World of Mathematics, Triangular Grid Graph
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

From Chai Wah Wu, May 30 2016: (Start)
a(n) = 3*a(n1)  3*a(n2) + a(n3) for n > 2.
G.f.: 2*(4*x^2 + 2*x  1)/(x  1)^3. (End)


MATHEMATICA

Table[3 n^2  3 n + 2, {n, 0, 100}] (* Vincenzo Librandi, Sep 05 2016 *)
LinearRecurrence[{3, 3, 1}, {2, 8, 20}, {0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
CoefficientList[Series[2 (1  2 x + 4 x^2)/(1 + x)^3, {x, 0, 20}], x] (* Eric W. Weisstein, Nov 29 2017 *)


PROG

(MAGMA) [3*n^2  3*n + 2: n in [0..70]]; // Vincenzo Librandi, Sep 05 2016
(PARI) a(n) = 3*n^23*n+2 \\ Altug Alkan, Sep 05 2016


CROSSREFS

A077588 is the same except for the initial term. Cf. A242659.
Sequence in context: A208966 A067640 A098277 * A080040 A060823 A178076
Adjacent sequences: A242655 A242656 A242657 * A242659 A242660 A242661


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, May 30 2014


STATUS

approved



