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A242971 Alternate n+1, 2^n. 1
1, 1, 2, 2, 3, 4, 4, 8, 5, 16, 6, 32, 7, 64, 8, 128, 9, 256, 10, 512, 11, 1024, 12, 2048, 13, 4096, 14, 8192, 15, 16384, 16, 32768, 17, 65536, 18, 131072, 19, 262144, 20, 524288, 21, 1048576, 22, 2097152, 23, 4194304, 24, 8388608, 25, 16777216, 26, 33554432 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The offset 0 is a choice. Another sequence could begin with A001477 instead of A000027. The Akiyama-Tanigawa transform applied to 1/(n+1) and 1/2^n are the second Bernoulli numbers A164555(n)/A027642(n) and the second (fractional) Euler numbers A198631(n)/A006519(n+1). (The first Euler numbers are not in the OEIS). Hence a(n).

a(2n+1) - a(2n) = 2^n -n -1 = 0, 0, 1, 4, 11,... = A000295(n) (Eulerian numbers).

a(2n+1) + a(2n) = 2^n +n +1 = A005126(n).

LINKS

Table of n, a(n) for n=0..51.

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-5,0,2).

FORMULA

a(n) = ((n+1) mod 2) * (n/2 + 1) + (n mod 2) * 2^((n-1)/2). - Wesley Ivan Hurt, Jun 29 2014

G.f.: (1 + x - x^2) * (1 - x^2 - x^3) / ((1 - x^2)^2 * (1 - 2*x^2)). - Michael Somos, Jun 30 2014

EXAMPLE

G.f. = 1 + x + 2*x^2 + 2*x^3 + 3*x^4 + 4*x^5 + 4*x^6 + 8*x^7 + 5*x^8 + ...

MAPLE

A242971:=n->((n+1) mod 2)*(n/2 + 1) + (n mod 2) * 2^((n-1)/2); seq(A242971(n), n=0..50); # Wesley Ivan Hurt, Jun 29 2014

MATHEMATICA

Table[Mod[n + 1, 2] (n/2 + 1) + Mod[n, 2] 2^((n - 1)/2), {n, 0, 50}] (* Wesley Ivan Hurt, Jun 29 2014 *)

CROSSREFS

Cf. A000027, A000079, A209308, A227577.

Sequence in context: A056099 A084848 A153937 * A036818 A036813 A036814

Adjacent sequences:  A242968 A242969 A242970 * A242972 A242973 A242974

KEYWORD

nonn

AUTHOR

Paul Curtz, Jun 22 2014

STATUS

approved

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Last modified December 10 23:33 EST 2018. Contains 318049 sequences. (Running on oeis4.)