A283104 Second differences of Stern's diatomic sequence (A002487).

-1, 1, -2, 3, -3, 2, -3, 5, -4, 3, -5, 6, -5, 3, -4, 7, -5, 4, -7, 9, -8, 5, -7, 10, -7, 5, -8, 9, -7, 4, -5, 9, -6, 5, -9, 12, -11, 7, -10, 15, -11, 8, -13, 15, -12, 7, -9, 14, -9, 7, -12, 15, -13, 8, -11, 15, -10, 7, -11, 12, -9, 5, -6, 11, -7, 6, -11, 15, -14, 9, -13, 20, -15, 11, -18, 21, -17, 10, -13, 21, -14, 11, -19

Offset

0,3

Links

Table of n, a(n) for n=0..82.

Michael Gilleland, Some Self-Similar Integer Sequences

Ilya Gutkovskiy, Extended graphical example

Eric Weisstein's World of Mathematics, Stern's Diatomic Series

Index entries for sequences related to Stern's sequences

Formula

G.f.: -1/x + ((1 - x)^2/x)*Product_{k>=0} (1 + x^(2^k) + x^(2^(k+1))).

Mathematica

Differences[a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 84}], 2]
CoefficientList[Series[-1/x + ((1 - x)^2/x) Product[1 + x^2^k + x^2^(k + 1), {k, 0, 20}], {x, 0, 82}], x]

Crossrefs

Cf. A002487, A070990.

Sequence in context: A242392 A002963 A046677 * A109747 A105612 A141744

Adjacent sequences: A283101 A283102 A283103 * A283105 A283106 A283107

Keyword

sign

Author

Ilya Gutkovskiy, Feb 28 2017

Status

approved