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A108296 Diagonal sums of the number triangle associated to A086617. 2
1, 1, 2, 3, 5, 8, 14, 24, 43, 78, 144, 269, 509, 971, 1868, 3618, 7049, 13805, 27162, 53661, 106405, 211697, 422458, 845386, 1696017, 3410522, 6873060, 13878721, 28077439, 56900936, 115501012, 234807488, 478032437, 974507543, 1989123814 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The triangle associated to A086617 is given by T(n,k)=if(k<=n, sum{j=0..n-k, C(n-k,j)C(k,j)C(j)},0). A050253(n)=A108296(n+2)-A108296(n).

LINKS

Table of n, a(n) for n=0..34.

FORMULA

G.f.: (1-x^2-sqrt(1-2x^2-4x^3-3x^4))/(2*x^3(1-x^2)); a(n)=sum{k=0..floor(n/2), sum{j=0..n-2k, C(n-2k, j)C(k, j)C(j)}.

Conjecture: (n+3)*a(n) +(-n-2)*a(n-1) +2*(-n-1)*a(n-2) +2*(-n+3)*a(n-3) +(n+1)*a(n-4) +3*(n-2)*a(n-5)=0. - R. J. Mathar, Nov 16 2012

CROSSREFS

Sequence in context: A038495 A007059 A079500 * A072100 A290075 A104882

Adjacent sequences:  A108293 A108294 A108295 * A108297 A108298 A108299

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 31 2005

STATUS

approved

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Last modified March 21 22:19 EDT 2019. Contains 321382 sequences. (Running on oeis4.)