A293344 a(n) = a(n-1) + a(n-3) + 2*a(n-5) - a(n-8) - a(n-10), n > 10.

1, 1, 4, 5, 16, 22, 29, 45, 76, 126, 210, 338, 534, 869, 1414, 2301, 3741, 6052, 9805, 15910, 25820, 41900, 67966, 110226, 178791, 290044, 470524, 763285, 1238156, 2008452, 3258039, 5285117, 8573382, 13907463, 22560169, 36596300, 59365317, 96300513

Offset: 1

Author

Eric M. Schmidt, Oct 12 2017

Keywords

• nonn
• easy

Comments

For n >= 5, gives the dimensions of a certain class of error-correcting codes. [Cascudo, Theorem 6.2]

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Ignacio Cascudo, On squares of cyclic codes, arXiv:1703.01267 [cs.IT], 2017.
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,0,2,0,0,-1,0,-1).

Crossrefs

Cf. A293343, A293345.

Programs

Mathematica

a = DifferenceRoot[Function[{a, n}, {a[n] + a[n+2] - 2*a[n+5] - a[n+7] - a[n+9] + a[n+10] == 0, a[1] == 1, a[2] == 1, a[3] == 4, a[4] == 5, a[5] == 16, a[6] == 22, a[7] == 29, a[8] == 45, a[9] == 76, a[10] == 126}]];
Table[a[n], {n, 1, 38}] (* Jean-François Alcover, Feb 24 2019 *)

PARI

Vec(x*(1 + 3*x^2 + 10*x^4 - 8*x^7 - 10*x^9) / (1 - x - x^3 - 2*x^5 + x^8 + x^10) + O(x^40)) \\ Colin Barker, Feb 24 2019

Formula

G.f.: x*(1 + 3*x^2 + 10*x^4 - 8*x^7 - 10*x^9) / (1 - x - x^3 - 2*x^5 + x^8 + x^10). - Colin Barker, Feb 24 2019