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Search: id:A002663
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| A002663 |
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2^n - C(n,0)- ... - C(n,3).
(Formerly M4152 N1725)
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+0
16
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| 0, 0, 0, 0, 1, 6, 22, 64, 163, 382, 848, 1816, 3797, 7814, 15914, 32192, 64839, 130238, 261156, 523128, 1047225, 2095590, 4192510, 8386560, 16774891, 33551806, 67105912, 134214424, 268431773, 536866822, 1073737298
(list; graph; listen)
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OFFSET
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0,6
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
J. Eckhoff, Der Satz von Radon in konvexen Productstrukturen II, Monat. f. Math., 73 (1969), 7-30.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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G.f.: x^4/((1-2*x)*(1-x)^4).
a(n)=sum{k=0..n, C(n, k+4)} = sum{k=4..n, C(n, k)}; a(n)=2a(n-1)+C(n-1, 3). - Paul Barry (pbarry(AT)wit.ie), Aug 23 2004
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MAPLE
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A002663:=-1/(2*z-1)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
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a=1; lst={}; s1=s2=s3=s4=0; Do[s1+=a; s2+=s1; s3+=s2; s4+=s3; AppendTo[lst, s4]; a=a*2, {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 10 2009]
Table[Sum[ Binomial[n + 4, k + 4], {k, 0, n}], {n, -4, 26}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2009]
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CROSSREFS
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a(n)= A055248(n, 4). Partial sums of A002662.
Cf. A000079, A000225, A000295, A002662, A002664, A035038-A035042.
Adjacent sequences: A002660 A002661 A002662 this_sequence A002664 A002665 A002666
Sequence in context: A053739 A055797 A001925 this_sequence A099855 A003469 A027992
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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