A173659 a(n) = a(n-1) + 8a(n-2) - 3a(n-3) - 17a(n-4) + a(n-5) + 13a(n-6) + 4a(n-7) - 6a(n-8) - a(n-9).

0, 0, 0, 1, 4, 9, 33, 79, 250, 647, 1914, 5157, 14797, 40663, 115036, 319098, 896896, 2498663, 7002446, 19546383, 54706009, 152839003, 427510168, 1194858679, 3341293220, 9340298995, 26116085175, 73010960431, 204132824544, 570699926244, 1595594838888

Offset

0,5

Links

Table of n, a(n) for n=0..30.

Wikipedia, Proton.

Formula

G.f.: x^2(x - 1)(x^4 + 4x^3 - x^2 - 4x - 1)/((x^3 + x^2 - 1)(x^6 + 5x^5 - 9x^4 - 3x^3 + 7x^2 + x - 1))

a(n) = a(n-1) + 8a(n-2) - 3a(n-3) - 17a(n-4) + a(n-5) + 13a(n-6) + 4a(n-7) - 6a(n-8) - a(n-9). [M. F. Hasler, Nov 24 2010]

M = {{0, 1, 0, 1, 0, 0, 0, 0, 0},

{0, 0, 1, 0, 1, 0, 0, 0, 0},

{1, 1, 0, 0, 0, 1, 0, 0, 0},

{1, 0, 0, 0, 0, 1, 1, 0, 0},

{0, 1, 0, 1, 0, 0, 0, 1, 0},

{0, 0, 1, 0, 1, 1, 0, 0, 1},

{0, 0, 0, 1, 0, 0, 0, 1, 0},

{0, 0, 0, 0, 1, 0, 0, 0, 1},

{0, 0, 0, 0, 0, 1, 1, 1, 0}};

v(n)=M.v(n-1) ; a(n) is the first component of v(n).

Mathematica

M = {{0, 1, 0, 1, 0, 0, 0, 0, 0},
      {0, 0, 1, 0, 1, 0, 0, 0, 0},
      {1, 1, 0, 0, 0, 1, 0, 0, 0},
      {1, 0, 0, 0, 0, 1, 1, 0, 0},
      {0, 1, 0, 1, 0, 0, 0, 1, 0},
      {0, 0, 1, 0, 1, 1, 0, 0, 1},
      {0, 0, 0, 1, 0, 0, 0, 1, 0},
      {0, 0, 0, 0, 1, 0, 0, 0, 1},
      {0, 0, 0, 0, 0, 1, 1, 1, 0}};
v[0] = {0, 0, 0, 0, 0, 0, 0, 0, 1};
v[n_] := v[n] = M.v[n - 1]
Table[v[n][[1]], {n, 0, 30}]

Crossrefs

Cf. A000931, A123589.

Sequence in context: A368683 A048757 A356825 * A054433 A219769 A308038

Adjacent sequences: A173656 A173657 A173658 * A173660 A173661 A173662

Keyword

nonn,easy,less

Author

Roger L. Bagula, Nov 24 2010

Extensions

Better name (using recurrence) from Joerg Arndt, Apr 06 2018

Status

approved