

A087079


Number of lunar partitions of n: number of ways of writing n as a lunar sum of distinct terms, ignoring order.


2



1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 1, 5, 22, 92, 376, 1520, 6112, 24512, 98176, 392960, 2, 22, 200, 1696, 13952, 113152, 911360, 7315456, 58621952, 469368832, 4, 92, 1696, 28928, 477184, 7749632, 124911616, 2005925888, 32153534464, 514926313472, 8
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OFFSET

0,3


COMMENTS

Without the condition that the numbers are distinct the answers are infinite because 1+1+1+...+1 = 1 in lunar arithmetic  see A087061.


LINKS

D Applegate and N. J. A. Sloane, Table of n, a(n) for n = 0..2000
D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic"  the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic"  the old name was too depressing]
D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
Index entries for sequences related to dismal (or lunar) arithmetic


FORMULA

For 1 <= a < 10 and 0 <= b < 10, a(10a+b) = 2^(ab+a+b1)+(2^a1)(2^b1)2^(ab1).  David Wasserman, Apr 14 2005


EXAMPLE

a(5) = 16: we can write 5 = 5 + any subset of {4, 3, 2, 1} (16 ways).
a(12) = 22: we can write 12 = 12 + any subset of {11, 10, 2, 1} (16 ways), 12 = 2 + 11 + 10 = 2 + 11 = 2 + 10 and those three with 1 added (6 ways).


PROG

(Pari/GP) A087079(n) = { my(v, r = 0, i, j, b); v = select(x > x != 0, digits(n)); for (i = 0, 2^#v  1, b = Vecrev(binary(i)); b = vector(#v, i, if (i <= #b, b[i], 0)); r += (1)^vecsum(b) * 2^prod(j = 1, #v, if (b[j] == 1, v[j], v[j] + 1)); ); r/2; } /* Jerome Raulin, Feb 15 2017 */


CROSSREFS

Cf. A010036.
The subsequence a(n) where n = 111..11 is A003465.  N. J. A. Sloane, May 21 2011.
Sequence in context: A251746 A251760 A243086 * A252757 A230579 A009694
Adjacent sequences: A087076 A087077 A087078 * A087080 A087081 A087082


KEYWORD

nonn


AUTHOR

Marc LeBrun, Oct 09 2003


EXTENSIONS

More terms from David Wasserman, Apr 14 2005


STATUS

approved



