A277252 a(n) = a(n-2) + a(n-3) + a(n-4) with a(0) = 0, a(1) = a(2) = 1, a(3) = 0.

0, 1, 1, 0, 2, 2, 3, 4, 7, 9, 14, 20, 30, 43, 64, 93, 137, 200, 294, 430, 631, 924, 1355, 1985, 2910, 4264, 6250, 9159, 13424, 19673, 28833, 42256, 61930, 90762, 133019, 194948, 285711, 418729, 613678, 899388, 1318118, 1931795, 2831184, 4149301, 6081097, 8912280, 13061582, 19142678, 28054959

Offset: 0

Author

Nicolas Bègue, Oct 07 2016

Keywords

• nonn

Comments

Limit a(n+1)/a(n) = 1.465571... (as in Narayana's cows sequence A000930).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1,1,1).

Crossrefs

Summed to A277253 equals A000930.

Programs

Maple

a:= n-> (<<0|1|0|0>, <0|0|1|0>,
          <0|0|0|1>, <1|1|1|0>>^n. <<0,1,1,0>>)[1,1]:
seq(a(n), n=0..50);  # Alois P. Heinz, Oct 07 2016

Mathematica

CoefficientList[Series[x*(1 + x - x^2)/(1 - x^2 - x^3 - x^4), {x, 0, 50}], x]
RecurrenceTable[{a[n] == a[n - 2] + a[n - 3] + a[n - 4], a[1] == 0,  a[2] == a[3] == 1, a[4] == 0}, a, {n, 52}]
LinearRecurrence[{0, 1, 1,1}, {0,1, 1, 0},52]

PARI

x='x+O('x^50); concat([0], Vec(x*(1+x-x^2)/(1-x^2-x^3-x^4))) \\ G. C. Greubel, May 02 2017

Formula

a(n) = a(n - 2) + a(n - 3) + a(n - 4).

G.f.: x*(1 + x - x^2)/(1 - x^2 - x^3 - x^4).

a(n) + A277253(n) = A000930(n).

Extensions

Corrected G.f. - G. C. Greubel, May 02 2017