A006062 Star-hex numbers. (Formerly M5265)

1, 37, 1261, 42841, 1455337, 49438621, 1679457781, 57052125937, 1938092824081, 65838103892821, 2236557439531837, 75977114840189641, 2580985347126915961, 87677524687474953037, 2978454854027021487301, 101179787512231255615201

Offset

1,2

References

M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 22.

H. J. Hindin, Stars, hexes, triangular numbers and Pythagorean triples, J. Rec. Math., 16 (1983/1984), 191-193.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..16.

H. J. Hindin, Stars, hexes, triangular numbers and Pythagorean triples, J. Rec. Math., 16 (1983/1984), 191-193. (Annotated scanned copy)

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Index entries for linear recurrences with constant coefficients, signature (35, -35, 1).

Formula

a(n) = 34*a(n-1) - a(n-2) + 4.

G.f.: -x*(x + 1)^2/(x - 1)/(x^2 - 34*x + 1). [from Simon Plouffe, see Maple code].

From Charlie Marion, Aug 03 2005: (Start)

a(n) = A001109(n-1)^2 + A001109(n)^2; e.g., 1261 = 6^2 + 35^2.

a(n) = A001652(n-1)*A046090(n-1) + A001653(n-1)^2; e.g., 1261 = 20*21 + 29^2. (End)

Maple

A006062:=-(z+1)**2/(z-1)/(z**2-34*z+1); [Simon Plouffe in his 1992 dissertation for offset zero.]

Crossrefs

Sequence in context: A099201 A218841 A246461 * A219420 A162851 A163220

Adjacent sequences: A006059 A006060 A006061 * A006063 A006064 A006065

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 11 1991

Status

approved