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A099572 Sum C(n-k+4,k), k=0..floor(n/2). 3
1, 1, 6, 7, 23, 30, 73, 103, 211, 314, 581, 895, 1560, 2455, 4135, 6590, 10890, 17480, 28590, 46070, 74946, 121016, 196326, 317342, 514123, 831465, 1346148, 2177613, 3524441, 5702054, 9227311, 14929365, 24157645, 39087010, 63245795, 102332805 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Fifth column of triangle A054450. In general sum{k=0..floor(n/2), binomial(n-k+r,k)}, r>=0, will have g.f. 1/((1-x^2)^r*(1-x-x^2)) and for r>0, a(n)=sum{k=0..n, F(n-k+1)*binomial(k/2+r-1,r-1)(1+(-1)^k)/2}.

LINKS

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (1,5,-4,-10,6,10,-4,-5,1,1).

FORMULA

G.f.: 1/((1-x^2)^4*(1-x-x^2)); - corrected by R. J. Mathar, Feb 20 2011

a(n)=sum{k=0..n, F(n-k+1)*binomial(k/2+3, 3)(1+(-1)^k)/2}.

CROSSREFS

Cf. A054451, A052952, A099571, A000045.

Sequence in context: A295729 A081284 A185509 * A288705 A287097 A281755

Adjacent sequences:  A099569 A099570 A099571 * A099573 A099574 A099575

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 23 2004

STATUS

approved

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Last modified November 15 11:18 EST 2019. Contains 329144 sequences. (Running on oeis4.)