A172316 7th column of the array A172119.

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

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