A341744 a(0)=1, a(1)=2; for n > 1, a(n) = a(n - a(n-2)) + n.

1, 2, 4, 5, 5, 6, 8, 9, 9, 10, 12, 13, 13, 14, 16, 17, 17, 18, 20, 21, 21, 22, 24, 25, 25, 26, 28, 29, 29, 30, 32, 33, 33, 34, 36, 37, 37, 38, 40, 41, 41, 42, 44, 45, 45, 46, 48, 49, 49, 50, 52, 53, 53, 54, 56, 57, 57, 58, 60, 61, 61, 62, 64, 65, 65, 66, 68, 69, 69, 70

Offset

0,2

Links

Table of n, a(n) for n=0..69.

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

Formula

a(n) = A130658(n) + n.

G.f.: (1 + 2*x^2 - x^3)/((1 - x)^2*(1 + x^2)). - Stefano Spezia, Feb 19 2021

Mathematica

A341744[n_] := Module[{a}, a[0] = 1; a[1] = 2; a[i_] := a[i] = a[i - a[i - 2]] + i; a[n]]; Table[A341744[n], {n, 0, 10}] (* José María Grau Ribas, Feb 18 2020, edited by Robert P. P. McKone, Feb 19 2021 *)
CoefficientList[Series[(1 + 2 x^2 - x^3)/((1 - x)^2*(1 + x^2)), {x, 0, 69}], x] (* Michael De Vlieger, Mar 19 2021 *)
LinearRecurrence[{2, -2, 2, -1}, {1, 2, 4, 5}, 90] (* Harvey P. Dale, Jun 19 2021 *)

Crossrefs

Cf. A004001, A087836, A193358, A209869, A274213, A130658.

Sequence in context: A256720 A091988 A023824 * A081252 A035559 A278480

Adjacent sequences: A341741 A341742 A341743 * A341745 A341746 A341747

Keyword

nonn,easy

Author

José María Grau Ribas, Feb 18 2021

Status

approved