A169973 a(n) = number of ways to write n as a sum of distinct numbers <= n, where the addition is carryless mod 10.

1, 1, 1, 2, 2, 4, 7, 13, 26, 51, 52, 103, 154, 205, 256, 308, 359, 410, 461, 512, 2408, 4814, 20276, 70298, 189440, 427728, 855452, 1583464, 2833460, 5127424, 10197920, 20395832, 42204112, 86360168, 173465856, 345264448, 687194480

Offset

0,4

Comments

a(0) = 1 by convention, as in A000009.

Without the restriction that the parts be distinct, the terms a(n) would be infinite: e.g. 5 = 5 + any number of copies of (1+2+3+4).

Links

Table of n, a(n) for n=0..36.

Index entries for sequences related to carryless arithmetic

Example

a(6) = 7: 6 = 6+5+4+1 = 6+5+3+2 = 6+4+3+2+1 = 5+1 = 4+2 = 3+2+1.
a(7) = 13: 7 = 6+1 = 5+2 = 4+3 = 4+2+1 = 7+6+4 = 7+6+3+1 = 7+5+4+1 = 7+5+3+2 = 7+4+3+2+1 = 6+5+4+2 = 6+5+3+2+1 = 7+6+5+4+3+2.

Crossrefs

Cf. A000009.

Sequence in context: A153970 A067953 A109070 * A300353 A049868 A120363

Adjacent sequences: A169970 A169971 A169972 * A169974 A169975 A169976

Keyword

nonn,base

Author

David Applegate, Marc LeBrun and N. J. A. Sloane, Jul 20 2010

Extensions

Missing initial a(0)=1 value inserted by Marc LeBrun, Oct 26 2010

Status

approved