A256963 Partial sums of A005210.

1, 2, 2, 4, 7, 8, 8, 14, 17, 22, 22, 24, 35, 36, 44, 50, 55, 56, 64, 74, 79, 82, 92, 100, 103, 110, 124, 124, 125, 154, 154, 180, 187, 212, 216, 234, 245, 254, 262, 276, 287, 290, 308, 328, 339, 344, 364, 382, 391, 396, 424, 438, 455, 464, 476, 502, 509, 510

Offset

1,2

Comments

It is conjectured that a(n) grows like n^2/6.

References

Popular Computing (Calabasas, CA), Z-Sequences, Vol. 4 (No. 42, Sep 1976), pp. 12-16.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Popular Computing (Calabasas, CA), Z-Sequences, continued. Annotated and scanned copy of pages 14, 15, 16, 18 of Vol. 5 (No. 56, Nov 1977).

Maple

b:= proc(n) option remember;
     `if`(n<3, 1, abs(b(n-1)+2*b(n-2)-n))
    end:
a:= proc(n) option remember;
      b(n)+`if`(n>1, a(n-1), 0)
    end:
seq(a(n), n=1..60);  # Alois P. Heinz, Apr 16 2015

Mathematica

Accumulate[RecurrenceTable[{a[1] == a[2] == 1, a[n] == Abs[a[n-1] + 2a[n-2] - n]}, a, {n, 1, 100}]] (* Jean-François Alcover, Nov 23 2020 *)

Crossrefs

Cf. A005210.

Sequence in context: A065968 A105669 A338917 * A355306 A019657 A134791

Adjacent sequences: A256960 A256961 A256962 * A256964 A256965 A256966

Keyword

nonn

Author

N. J. A. Sloane, Apr 16 2015

Status

approved