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A116082
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C(n,7) + C(n,6) + C(n,5) + C(n,4) + C(n,3) + C(n,2) + C(n,1).
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2
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0, 1, 3, 7, 15, 31, 63, 127, 254, 501, 967, 1815, 3301, 5811, 9907, 16383, 26332, 41225, 63003, 94183, 137979, 198439, 280599, 390655, 536154, 726205, 971711, 1285623, 1683217, 2182395, 2804011, 3572223, 4514872, 5663889, 7055731, 8731847
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| Michael Boardman, The Egg-Drop Numbers, Mathematics Magazine, 77 (2004), 368-372. See Table 2 on page 370. [From Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Jun 18 2009]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
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FORMULA
| a(n) = n*(n^6-14*n^5+112*n^4-350*n^3+1099*n^2+364*n+3828)/5040. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 14 2006
G.f. x*(1-5*x+11*x^2-13*x^3+9*x^4-3*x^5+x^6) /(1-x)^8 . - R. J. Mathar, Jun 20 2011
a(0)=0, a(1)=1, a(2)=3, a(3)=7, a(4)=15, a(5)=31, a(6)=63, a(7)=127, a(n)=8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+ 8*a(n-7)- a(n-8) [From Harvey P. Dale, Aug 05 2011]
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MAPLE
| a:=n->n*(n^6-14*n^5+112*n^4-350*n^3+1099*n^2+364*n+3828)/5040: seq(a(n), n=0..35); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 14 2006
seq(sum(binomial(n, k), k=1..7), n=0..35); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 14 2007
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MATHEMATICA
| Table[Total[Binomial[n, Range[7]]], {n, 0, 40}] (* or *) LinearRecurrence[ {8, -28, 56, -70, 56, -28, 8, -1}, {0, 1, 3, 7, 15, 31, 63, 127}, 41](* From Harvey P. Dale, Aug 05 2011 *)
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PROG
| (MAGMA) [n*(n^6-14*n^5+112*n^4-350*n^3+1099*n^2+364*n+3828)/5040: n in [0..40]]; // Vincenzo Librandi, Jun 21 2011
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CROSSREFS
| a(n) = A000580(n) + A000579(n) + A000389(n) + A000332(n) + A000292(n) + A000217(n) + n. a(n) = A000580(n) + A115567(n).
A000217, A000225, A004006, A055795, A057703, A115567, A116082 [From Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Jun 18 2009]
Sequence in context: A147596 A115567 A043740 * A043747 A105754 A116690
Adjacent sequences: A116079 A116080 A116081 * A116083 A116084 A116085
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 13 2006
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