A276275 Padovan like sequence: a(n) = a(n-2) + a(n-3) for n>3, a(1)=2, a(2)=2, a(3)=0.

2, 2, 0, 4, 2, 4, 6, 6, 10, 12, 16, 22, 28, 38, 50, 66, 88, 116, 154, 204, 270, 358, 474, 628, 832, 1102, 1460, 1934, 2562, 3394, 4496, 5956, 7890, 10452, 13846, 18342, 24298, 32188, 42640, 56486, 74828, 99126, 131314, 173954, 230440, 305268, 404394, 535708

Offset

1,1

Comments

Obtained from Padovan Spiral number (A134816) modulo 3 reduction periodic sequence 1112201210010, 111 112 122 220 ... fourth initialization values 220, it satisfies the same recurrence a(n) = a(n-2) + a(n-3).

Links

Table of n, a(n) for n=1..48.

Index entries for linear recurrences with constant coefficients, signature (0,1,1).

Formula

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

a(n) = A134816(n) + A007307(n-3) for n>=4.

a(n) = 2*A084338(n-3) for n>=4.

Mathematica

RecurrenceTable[{a[n] == a[n - 2] + a[n - 3], a[1] == 2, a[2] == 2, a[3] == 0}, a, {n, 1, 48}] (* or *) CoefficientList[Series[2 x (1 + x - x^2)/(1 - x^2 - x^3), {x, 0, 47}], x] (* Michael De Vlieger, Sep 02 2016 *)
LinearRecurrence[{0, 1, 1}, {2, 2, 0}, 60] (* Harvey P. Dale, Jan 27 2023 *)

Crossrefs

Cf. A134816, A084338.

Sequence in context: A098268 A330347 A329681 * A128585 A217840 A181615

Adjacent sequences: A276272 A276273 A276274 * A276276 A276277 A276278

Keyword

nonn,easy

Author

Nicolas Bègue, Aug 26 2016

Status

approved