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A172316 7th column of the array A172119. 6
1, 2, 4, 8, 16, 32, 64, 127, 252, 500, 992, 1968, 3904, 7744, 15361, 30470, 60440, 119888, 237808, 471712, 935680, 1855999, 3681528, 7302616, 14485344, 28732880, 56994048, 113052416, 224248833, 444816138, 882329660 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
O. Dunkel, Solutions of a probability difference equation, Amer. Math. Monthly, 32 (1925), 354-370; see p. 356 with r = 6.
FORMULA
G.f.: 1/(1 - 2*z + z^7).
Recurrence formula: a(n+7) = 2*a(n+6) - a(n).
a(n) = Sum_{j=0..floor(n/(k+1))} ((-1)^j*binomial(n-k*j,n-(k+1)*j)*2^(n-(k+1)*j)) with k=6.
EXAMPLE
a(3) = binomial(3,3)*2^3 = 8.
a(7) = binomial(7,7)*2^7 - binomial(1,0)*2^0 = 127.
MAPLE
for k from 0 to 20 do for n from 0 to 30 do b(n):=sum((-1)^j*binomial(n-k*j, n-(k+1)*j)*2^(n-(k+1)*j), j=0..floor(n/(k+1))):od:k: seq(b(n), n=0..30):od; k:=6:taylor(1/(1-2*z+z^(k+1)), z=0, 30);
CROSSREFS
Sequence in context: A145113 A062257 A208127 * A062258 A239560 A066178
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Jan 31 2010
STATUS
approved

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Last modified June 25 10:55 EDT 2024. Contains 373701 sequences. (Running on oeis4.)