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A084635 Binomial transform of 1,0,1,0,1,1,1,... 3
1, 1, 2, 4, 8, 17, 38, 86, 192, 419, 894, 1872, 3864, 7893, 16006, 32298, 64960, 130375, 261310, 523300, 1047416, 2095801, 4192742, 8386814, 16775168, 33552107, 67106238, 134214776, 268432152, 536867229, 1073737734, 2147479122 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The sequence 1,2,4... has a(n)=2^(n+1)-(n^3+5n+6)/6 =sum{k=0..3,C(n,k)}+2*sum{k=4..n,C(n,k)}. It is the binomial transform of 1,1,1,1,2,2,2,2,2...

LINKS

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-9,2).

FORMULA

a(n)=2^n-n(n^2-3n+8)/6; a(n)=1+C(n, 2)+sum{k=4..n, C(n, k)}.

O.g.f.: (-5x+10x^2-10x^3+5x^4+1)/[(-1+x)^4*(1-2x)]. - R. J. Mathar, Apr 02 2008

CROSSREFS

Cf. A000325, A084634.

Sequence in context: A212658 A036374 A214999 * A294529 A154222 A114199

Adjacent sequences:  A084632 A084633 A084634 * A084636 A084637 A084638

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jun 06 2003

STATUS

approved

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Last modified November 17 23:26 EST 2019. Contains 329242 sequences. (Running on oeis4.)