A134522 a(n) = 2^n + ceiling(n/2).

1, 3, 5, 10, 18, 35, 67, 132, 260, 517, 1029, 2054, 4102, 8199, 16391, 32776, 65544, 131081, 262153, 524298, 1048586, 2097163, 4194315, 8388620, 16777228, 33554445, 67108877, 134217742, 268435470, 536870927, 1073741839, 2147483664, 4294967312, 8589934609

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (3, -1, -3, 2).

Formula

From Andrew Howroyd, Aug 10 2018: (Start)

a(n) = A000079(n) + A110654(n).

a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4).

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

(End)

a(n) = Sum_{k=1..n+1} C(n+1,k)^(k mod 2). - Wesley Ivan Hurt, Nov 20 2021

Prog

(PARI) a(n)=2^n + (n+1)\2; \\ Andrew Howroyd, Aug 10 2018
(PARI) Vec((1 - 3*x^2 + x^3)/((1 - x)^2*(1 + x)*(1 - 2*x)) + O(x^40)) \\ Andrew Howroyd, Aug 10 2018

Crossrefs

Row sums of A134521.

Cf. A000079, A110654.

Sequence in context: A154949 A318248 A107232 * A001445 A192860 A125750

Adjacent sequences: A134519 A134520 A134521 * A134523 A134524 A134525

Keyword

nonn,easy

Author

Gary W. Adamson, Oct 29 2007

Extensions

Name changed, a(8) inserted and a(14)-a(33) from Andrew Howroyd, Aug 10 2018

Status

approved