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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 Table of n, a(n) for n=0..30. O. Dunkel, Solutions of a probability difference equation, Amer. Math. Monthly, 32 (1925), 354-370; see p. 356 with r = 6. Index entries for linear recurrences with constant coefficients, signature (2,0,0,0,0,0,-1) 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 Cf. A000071, A001949, A008937, A107066, A172119. Sequence in context: A145113 A062257 A208127 * A062258 A239560 A066178 Adjacent sequences: A172313 A172314 A172315 * A172317 A172318 A172319 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.)