The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A288310 a(0) = a(1) = 1; a(2*n) = a(n) - a(n-1), a(2*n+1) = Sum_{k=0..n} a(n-k). 0
 1, 1, 0, 2, -1, 2, 2, 4, -3, 3, 3, 5, 0, 7, 2, 11, -7, 8, 6, 11, 0, 14, 2, 19, -5, 19, 7, 26, -5, 28, 9, 39, -18, 32, 15, 40, -2, 46, 5, 57, -11, 57, 14, 71, -12, 73, 17, 92, -24, 87, 24, 106, -12, 113, 19, 139, -31, 134, 33, 162, -19, 171, 30, 210, -57, 192, 50, 224, -17, 239, 25 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Sequence has its first differences and its partial sums as bisections. LINKS Table of n, a(n) for n=0..70. Michael Gilleland, Some Self-Similar Integer Sequences FORMULA a(n) = Sum_{k=0..n} a(2*k). a(n) = a(2*n+1) - a(2*n-1). a(2*n+1) = Sum_{k=0..n} Sum_{m=0..k} a(2*m). EXAMPLE a(0) = a(1) = 1 by definition; a(2) = a(2*1) = a(1) - a(0) = 0; a(3) = a(2*1+1) = a(0) + a(1) = 2; a(4) = a(2*2) = a(2) - a(1) = -1; a(5) = a(2*2+1) = a(0) + a(1) + a(2) = 2; a(6) = a(2*3) = a(3) - a(2) = 2, etc. MATHEMATICA a[0] = 1; a[1] = 1; a[n_] := a[n] = If[EvenQ[n], a[n/2] - a[(n - 2)/2], Sum[a[(n - 1)/2 - k], {k, 0, (n - 1)/2}]]; Table[a[n], {n, 0, 70}] PROG (Python) def a(n): return 1 if n<2 else a(n/2) - a(n/2 - 1) if n%2==0 else sum([a((n - 1)/2 - k) for k in range((n + 1)/2)]) # Indranil Ghosh, Jun 08 2017 CROSSREFS Cf. A030067, A086449, A086450, A109671. Sequence in context: A131183 A346063 A133770 * A332718 A341461 A337485 Adjacent sequences: A288307 A288308 A288309 * A288311 A288312 A288313 KEYWORD sign AUTHOR Ilya Gutkovskiy, Jun 07 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 12 03:27 EDT 2024. Contains 375085 sequences. (Running on oeis4.)