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A242658
a(n) = 3*n^2 - 3*n + 2.
4
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
OFFSET
0,1
COMMENTS
An exercise in Smith (1950), my secondary school algebra book.
For n > 0, also the number of (not necessarily maximal) cliques in the (n-1)-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
Eric Weisstein's World of Mathematics, Clique
Eric Weisstein's World of Mathematics, Triangular Grid Graph
FORMULA
From Chai Wah Wu, May 30 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
G.f.: 2*(-4*x^2 + 2*x - 1)/(x - 1)^3. (End)
E.g.f.: exp(x)*(2 + 3*x^2). - Stefano Spezia, Dec 27 2021
a(n) = A002378(n) + A002378(n-1) + A002378(n-2). - Peter Bala, Jun 11 2024
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^2-3*n+2 \\ Altug Alkan, Sep 05 2016
CROSSREFS
A077588 is the same except for the initial term.
Sequence in context: A208966 A067640 A098277 * A080040 A060823 A330645
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 30 2014
STATUS
approved