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 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 (list; graph; refs; listen; history; text; internal format)
 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. FORMULA For 1 <= a < 10 and 0 <= b < 10, a(10a+b) = 2^(ab+a+b-1)+(2^a-1)(2^b-1)2^(ab-1). - 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

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Last modified October 17 15:32 EDT 2019. Contains 328116 sequences. (Running on oeis4.)