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A099099 Quadrisection of a generalized Padovan sequence. 1
1, 1, 1, 2, 6, 16, 37, 80, 172, 377, 839, 1874, 4175, 9274, 20577, 45665, 101393, 225193, 500162, 1110790, 2466760, 5477917, 12164896, 27015092, 59993817, 133231279, 295872778, 657057431, 1459155634, 3240410561, 7196122817 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Quadrisection of sequence with g.f. 1/(1 - x^3 - x^4), or A017817.

LINKS

Table of n, a(n) for n=0..30.

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

FORMULA

G.f.: (1-x)^3/((1-x)^4-x^3).

a(n) = sum_{k=0..2n} binomial(k, 4n-3k).

a(n) = 4a(n-1) - 6a(n-2) + 5a(n-3) - a(n-4).

a(n) = A017817(4n).

a(n) = sum_{k=0..floor((n+1)/2)} binomial(n+k, 4k). - Paul Barry, May 09 2005

MATHEMATICA

Join[{1}, a=0; b=0; c=0; d=1; Table[a+=b; b+=c; c+=d; d+=a, {n, 50}]] (* Vladimir Joseph Stephan Orlovsky, Nov 19 2010 *)

CROSSREFS

Sequence in context: A306332 A026540 A128232 * A074082 A212383 A097813

Adjacent sequences:  A099096 A099097 A099098 * A099100 A099101 A099102

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 29 2004

STATUS

approved

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Last modified March 26 16:33 EDT 2019. Contains 321510 sequences. (Running on oeis4.)