A137280 a(n) = 3*a(n-1) + 7*a(n-2), with a(1) = 1, a(2) = 10.

1, 10, 37, 181, 802, 3673, 16633, 75610, 343261, 1559053, 7079986, 32153329, 146019889, 663132970, 3011538133, 13676545189, 62110402498, 282067023817, 1280973888937, 5817390833530, 26418989723149, 119978705004157, 544869043074514, 2474458064252641, 11237457494279521

Offset: 1

Author

Gary W. Adamson, Mar 14 2008

Keywords

• nonn
• easy

Comments

a(n) == 1 mod 9.

a(n)/a(n-1) tends to 4.54138126... = (3 + sqrt(37))/2.

Examples

			a(4) = 181 = 3*a(3) + 7*a(2) = 3*37 + 7*10.
a(4) = 181 = upper left term in [1,3; 3,2]^4.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500
• Index entries for linear recurrences with constant coefficients, signature (3,7)

Programs

Mathematica

LinearRecurrence[{3, 7}, {1, 10}, 25] (* Paolo Xausa, Jan 15 2025 *)

Formula

a(1) = 1, a(2) = 10, a(n) = 3*a(n-1) + 7*a(n-2) for n>2.

a(n) = upper left term in [1,3; 3,2]^n

From R. J. Mathar, Mar 17 2008: (Start)

O.g.f.: x*(1+7*x)/(1-3*x-7*x^2).

a(n) = A015524(n) + 7*A015524(n-1). (End)

Extensions

a(23) onwards from Andrew Howroyd, Jan 12 2025