A131322 Row sums of triangle A131321.

1, 1, 3, 5, 12, 23, 51, 103, 221, 456, 965, 2009, 4227, 8833, 18540, 38803, 81363, 170399, 357145, 748176, 1567849, 3284833, 6883059, 14421533, 30218028, 63314735, 132664227, 277968871, 582428789, 1220356440, 2557009709

Offset

0,3

Comments

Equals INVERT transform of (1, 2, 0, 1, 0, 1, 0, 1, ...). - Gary W. Adamson, Apr 28 2009

The sequence is also the INVERT transform of the aerated odd-indexed Fibonacci numbers (i.e., of (1, 0, 2, 0, 5, 0, ...)). Sequence A124400 is the INVERT transform of the aerated even-indexed Fibonacci numbers. - Gary W. Adamson, Feb 07 2014

Links

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

Formula

G.f.: (1-x^2)/(1 - x - 3x^2 + x^3 + x^4). - Philippe Deléham, Jan 21 2012

a(n) = a(n-1) + 3*a(n-2) - a(n-3) - a(n-4), a(0)=1, a(1)=1, a(2)=3, a(3)=5. - Philippe Deléham, Jan 21 2012

a(n) = Sum_{m=0..ceiling(n/2)} binomial(n-m,n-2*m)*Fibonacci(n-2*m+1). - Vladimir Kruchinin, Jan 26 2013

Example

a(4) = 12 = 5 + 0 + 6 + 0 + 1.

Crossrefs

Cf. A131321, A000045.

Cf. A124400.

Sequence in context: A247794 A034758 A215109 * A224747 A036657 A047761

Adjacent sequences: A131319 A131320 A131321 * A131323 A131324 A131325

Keyword

nonn

Author

Gary W. Adamson, Jun 28 2007

Extensions

a(10)-a(30) from Philippe Deléham, Jan 21 2012

Status

approved