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Search: id:A038505
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| A038505 |
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Sum of every 4th entry of row n in Pascal's triangle, starting at "n choose 2". |
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+0
15
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| 0, 1, 3, 6, 10, 16, 28, 56, 120, 256, 528, 1056, 2080, 4096, 8128, 16256, 32640, 65536, 131328, 262656, 524800, 1048576, 2096128, 4192256, 8386560, 16777216, 33558528, 67117056, 134225920, 268435456, 536854528, 1073709056
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of strings over Z_2 of length n with trace 0 and subtrace 1.
Same as number of strings over GF(2) of length n with trace 0 and subtrace 1.
Binomial transform of (0,1,1,0,0,1,1,0,...) - Paul Barry (pbarry(AT)wit.ie), Jul 07 2003
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LINKS
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F. Ruskey, Strings over Z_2 of given Trace and Subtrace
F. Ruskey, Strings over GF(2) of given Trace and Subtrace
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FORMULA
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a(n)=sum{k=0..n+1, (1/2)C(n+1, k)(-1)^C(k+3, 3)} - Paul Barry (pbarry(AT)wit.ie), Jul 07 2003
G.f. : x(1-x)/((1-x)^4-x^4); a(n)=sum{k=0..floor((n+1)/2), binomial(n+1, 2k)(1-(-1)^k)/2}. - Paul Barry (pbarry(AT)wit.ie), Nov 29 2004
Conjecture: 2*a(n+2) = A038504(n+3) + A000749(n+3) + 2*A009545(n+1) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), May 22 2005
a(n; t, s) = a(n-1; t, s) + a(n-1; t+1, s+t+1) where t is the trace and s is the subtrace.
a(n)=4a(n-1)-6a(n-2)+4a(n-3), n > 3; sequence is identical to its fourth differences. - Paul Curtz (bpcrtz(AT)free.fr), Dec 21 2007
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EXAMPLE
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a(3;0,1)=3 since the three binary strings of trace 0, subtrace 1 and length 3 are { 011, 101, 110 }.
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CROSSREFS
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Cf. A038503, A038504, A000749.
Cf. A009116.
Sequence in context: A130578 A107068 A033541 this_sequence A119971 A094272 A005045
Adjacent sequences: A038502 A038503 A038504 this_sequence A038506 A038507 A038508
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KEYWORD
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easy,nonn
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AUTHOR
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Frank Ruskey (fruskey(AT)cs.uvic.ca)
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