A038621 Growth function of an infinite cubic graph (number of nodes at distance <=n from fixed node).

1, 4, 10, 22, 46, 81, 129, 198, 284, 392, 530, 691, 883, 1114, 1374, 1674, 2022, 2405, 2837, 3326, 3856, 4444, 5098, 5799, 6567, 7410, 8306, 9278, 10334, 11449, 12649, 13942, 15300, 16752, 18306, 19931, 21659, 23498, 25414, 27442, 29590, 31821, 34173, 36654

Offset: 0

Author

Jan Kristian Haugland

Keywords

• nonn
• easy

Comments

Partial sums of A038620.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).

Crossrefs

Cf. A038620, A290705.

Programs

Mathematica

CoefficientList[Series[(x + 1) (2 x^8 - 4 x^7 + 3 x^6 - x^5 + 6 x^4 + 2 x^3 + 2 x^2 + x + 1)/((x - 1)^4 (x^2 + x + 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 22 2013 *)
LinearRecurrence[{2,-1,2,-4,2,-1,2,-1},{1,4,10,22,46,81,129,198,284,392},50] (* Harvey P. Dale, Sep 03 2016 *)

Formula

a(0)=1, a(1)=4; for n>=2: if n == 0 (mod 3), a(n) = (4*n^3 + 6*n^2 + 15*n - 9)/9; if n == 1 (mod 3), a(n) = (4*n^3 + 6*n^2 + 18*n - 10)/9; if n == 2 (mod 3), a(n) = (4*n^3 + 6*n^2 + 15*n + 4)/9.

G.f.: (x+1)*(2*x^8-4*x^7+3*x^6-x^5+6*x^4+2*x^3+2*x^2+x+1) / ((x-1)^4*(x^2+x+1)^2). - Colin Barker, May 10 2013

Extensions

More terms from Colin Barker, May 10 2013