A099099 Quadrisection of a generalized Padovan sequence.

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

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: A329256 A128232 A362352 * A074082 A212383 A333881

Adjacent sequences: A099096 A099097 A099098 * A099100 A099101 A099102

Keyword

easy,nonn

Author

Paul Barry, Sep 29 2004

Status

approved