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A131322 Row sums of triangle A131321. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 27 19:04 EDT 2020. Contains 337388 sequences. (Running on oeis4.)