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

0,2

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).

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

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 *)

Crossrefs

Cf. A038620, A290705.

Sequence in context: A265052 A266372 A174622 * A078407 A347113 A347307

Adjacent sequences: A038618 A038619 A038620 * A038622 A038623 A038624

Keyword

nonn,easy

Author

Jan Kristian Haugland

Extensions

More terms from Colin Barker, May 10 2013

Status

approved